List of weight distributions

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This is a list of weight distributions in the OEIS.

Overview

For technical reasons, the list below is in reverse alphabetical order. More explanations and background information will be given on the "main page" weight distributions.

Reed-Müller codes

A141085 Weight distribution of [256,37,64] Reed-Muller (or RM) code.

1, 0, 0, 0, 0, 0, 0, 0, 43180, 0, 0, 0, 89952576, 0, 9594941440, 28897705984, 60273667110, 28897705984, 9594941440, 0, 89952576, 0, 0, 0, 43180, 0, 0, 0, 0, 0, 0, 0, 1

A147314 Weight distribution of [512,46,128] Reed-Muller (or RM) code.

1, 0, 0, 0, 0, 0, 0, 0, 173740, 0, 0, 0, 1482766656, 0, 700430725120, 14766727757824, 39431461330982, 14766727757824, 700430725120, 0, 1482766656, 0, 0, 0, 173740, 0, 0, 0, 0, 0, 0, 0, 1

A146953 Weight distribution of [256,93,32] Reed-Muller (or RM) code.

1, 0, 0, 0, 777240, 0, 2698577280, 304296714240, 74984804718940, 707415842488320, 28055013884190720, 764244915168215040, 20661827603503720320, 414411510493363568640, 6266131517201901649920

A146976 Weight distribution of [256,163,16] Reed-Muller (or RM) code.

1, 0, 0, 0, 0, 0, 0, 0, 3212592, 0, 0, 0, 12593360640, 0, 1518742159360, 1684323434496, 233496616617720, 2063296207257600, 54280709965103104, 1024338139923087360, 25271993786704661248, 603379495807494389760

A147531 Weight distribution of [512,130,64] Reed-Muller (or RM) code.

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6304280, 0, 0, 0, 0, 0, 0, 0, 91931532672, 0, 0, 0, 27817105940480, 0, 29533455515648, 0, 12583593752692060, 0, 361519028967047168, 0, 17833197403694489600, 12590654537544499200

Reed-Muller codes of higher order

A001726 Weight distribution of [ 64,22,16 ] 2nd order Reed-Muller code of length 64.

1, 0, 0, 0, 2604, 0, 291648, 888832, 1828134, 888832, 291648, 0, 2604, 0, 0, 0, 1

A001727 Weight distribution of [ 64,42,8 ] 3rd order Reed-Muller code of length 64.

1, 0, 0, 0, 11160, 0, 1749888, 22855680, 232081500, 1717223424, 9366150528, 38269550592, 119637587496, 286573658112, 533982211840, 771854598144, 874731154374, 771854598144, 533982211840, 286573658112

A006006 Weight distribution of [ 128,29,32 ] 2nd order Reed-Muller code.

1, 0, 0, 0, 10668, 0, 5291328, 112881664, 300503590, 112881664, 5291328, 0, 10668, 0, 0, 0, 1

A006028 Weight distribution of [ 128,99,8 ] 4th order Reed-Muller code RM(4,7).

1, 0, 0, 0, 188976, 0, 148157184, 5805342720, 352501184760, 14090340827136, 445990551166720, 11148730324353024, 224814298345622160, 3704888469231108096, 50486579825291883008, 574502111223143792640, 5505259862572668584988

A018895 Weight distribution of [ 512,130,64 ] third-order Reed-Muller code.

1, 0, 0, 0, 0, 0, 0, 0, 6304280, 91931532672, 27817105940480, 29533455515648, 12583593752692060, 361519028967047168, 17833197403694489600, 12590654537544499200, 1020786087075313090560, 4318594506377763225600

(Check if A018896 is not missing here.)

A018897 Weight distribution of [512,382,16] 9th-order Reed-Muller (or RM) code.

1, 0, 0, 0, 0, 0, 0, 0, 105911904, 0, 0, 0, 1838630653440, 0, 509913567887360, 1721378550054912, 131916883632582384, 2108688723817267200, 74239828158397841408, 1712014250742613278720

Rao-Reddy code

A031136 Weight distribution of [ 48,17,12 ] dual Rao-Reddy code.

1, 0, 0, 0, 0, 0, 80, 0, 3063, 7168, 14640, 21504, 38160, 21504, 14640, 7168, 3063, 0, 80, 0, 0, 0, 0, 0, 1

A031137 Weight distribution of [48,23,8] Rao-Reddy code.

1, 0, 0, 0, 7530, 92160, 1080384, 7342080, 34408911, 111507456, 255566784, 417404928, 492663180, 417404928, 255566784, 111507456, 34408911, 7342080, 1080384, 92160, 7530, 0, 0, 0, 1

QR codes

Overview of QR codes

(TO DO: Add some general explanations here.)

The remainder of this subsection is divided up in three parts: binary QR codes, extended binary QR codes, and ternary QR codes.

binary quadratic-residue codes

(A-numbers A001381, A024881, A028381-A028385, ..., A145922-A146888.)

A001381 Weight distribution of binary [ 48,24,12 ] quadratic residue code.

1, 0, 0, 17296, 535095, 3995376, 7681680, 3995376, 535095, 17296, 0, 0, 1

A024881 Weight distribution of [ 17,8,6 ] binary quadratic-residue code.

1, 0, 0, 68, 85, 68, 34

A028381 Weight distribution of [ 17,9,5 ] binary quadratic-residue code.

1, 0, 0, 0, 0, 34, 68, 68, 85, 85, 68, 68, 34, 0, 0, 0, 0, 1

A028382 Weight distribution of [ 31,16,7 ] binary BCH and quadratic-residue codes.

1, 0, 0, 0, 0, 0, 0, 155, 465, 0, 0, 5208, 8680, 0, 0, 18259, 18259, 0, 0, 8680, 5208, 0, 0, 465, 155, 0, 0, 0, 0, 0, 0, 1

A028383 Weight distribution of [ 31,15,8 ] binary quadratic-residue code.

1, 0, 465, 8680, 18259, 5208, 155

A028384 Weight distribution of [ 47,24,11 ] binary quadratic-residue code.

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4324, 12972, 0, 0, 178365, 356730, 0, 0, 1664740, 2330636, 0, 0, 3840840, 3840840, 0, 0, 2330636, 1664740, 0, 0, 356730, 178365, 0, 0, 12972, 4324, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1

A028385 Weight distribution of [ 47,23,12 ] binary quadratic-residue code.

1, 0, 0, 12972, 356730, 2330636, 3840840, 1664740, 178365, 4324

A033869 Weight distribution of [79,40,15] binary quadratic-residue (or QR) code.

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 19513, 78052, 0, 0, 3220672, 9662016, 0, 0, 177021936, 413051184, 0, 0, 3705860928, 6882313152, 0, 0, 31883071220, 47824606830, 0, 0, 118486682496, 144817056384, 0, 0, 195553169504

A069646 Weight distribution of [97,49,15] binary quadratic-residue (or QR) code.

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4656, 23862, 14841, 65960, 190120, 741468, 3375988, 11662504, 40893648, 126088748, 360406410, 998048520, 2614461952, 6536154880, 15589859400, 35337014640, 76345991760, 157463608005

A072189 Weight distribution of [103,52,19] binary quadratic-residue (or QR) code.

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 218875, 919275, 0, 0, 47592180, 158640600, 0, 0, 4283380248, 11626317816, 0, 0, 174684872920, 393040964070, 0, 0, 3432179437380, 6483005603940, 0, 0, 33982965303425, 54372744485480

A076710 Weight distribution of [137,69,21] binary quadratic-residue (or QR) code.

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 51238, 270164, 409904, 1947044, 4057118, 17476816, 99448300, 390689750, 1445284240, 5203023264, 18055712240, 59809546795, 189973513945, 581095454420, 1709208146190

A080953 Weight distribution of [151,76,19] binary quadratic-residue (or QR) code.

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3775, 24915, 0, 0, 113250, 604000, 0, 0, 30256625, 133993625, 0, 0, 8292705580, 31097645925, 0, 0, 1302257122605, 4196161839505, 0, 0, 113402818847850, 317527892773980, 0

A091536 Weight distribution of [89,45,17] binary quadratic-residue (or QR) code.

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 54824, 219296, 626560, 2192960, 7462917, 23067198, 66429244, 182680421, 476804328, 1173672192, 2739870518, 6066856147, 12753805999, 25507611998, 48541216592

A106433 Weight distribution of [113,57,15] binary quadratic-residue (or QR) code.

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3616, 22148, 79100, 371770, 539462, 2255932, 7723324, 28962465, 106963766, 362031208, 1164652580, 3577147210, 10584922440, 29637782832, 79257402672, 203097094347, 498291292415

A134975 Weight distribution of [127,64,19] binary quadratic-residue (or QR) code.

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8890, 48006, 0, 0, 2416302, 10470642, 0, 0, 642229602, 2293677150, 0, 0, 80124107595, 240372322785, 0, 0, 5082581311830, 12988818908010, 0, 0, 172664602751130, 379862126052486, 0

A145922 Weight distribution of [71,36,13] binary quadratic-residue (or QR) code.

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 497, 2485, 0, 0, 47570, 166495, 0, 0, 5084310, 13219206, 0, 0, 154102305, 308204610, 0, 0, 1710651635, 2688166855, 0, 0, 7377935180, 9222418975, 0, 0, 12879738244, 12879738244, 0, 0, 9222418975

A145981 Weight distribution of [71,36,11] binary quadratic-residue (or QR) code.

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 497, 2485, 47570, 166495, 5084310, 13219206, 154102305, 308204610, 1710651635, 2688166855, 7377935180, 9222418975, 12879738244, 12879738244, 9222418975, 7377935180, 2688166855

A145982 Weight distribution of [73,37,13] binary quadratic-residue (or QR) code.

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1533, 6570, 19272, 69861, 266085, 827820, 2292200, 6188940, 15841584, 37443744, 82642716, 172172325, 337713987, 623471976, 1086405418, 1784808901, 2766489030, 4057517244, 5630090544

A146075 Weight distribution of [41,21,9] binary quadratic-residue (or QR) code.

1, 0, 0, 0, 0, 0, 0, 0, 0, 410, 1312, 3034, 7585, 16605, 33210, 60024, 97539, 146370, 195160, 232060, 255266, 255266, 232060, 195160, 146370, 97539, 60024, 33210, 16605, 7585, 3034, 1312, 410, 0, 0, 0, 0, 0, 0, 0, 0, 1

A146888 Weight distribution of [167,84,23] binary quadratic-residue (or QR) code.

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 110888, 665328, 0, 0, 3021698, 15108490, 0, 0, 1057206192, 4493126316, 0, 0, 268132007628, 983150694636, 0, 0, 39540857275985, 126530743283152, 0, 0

binary extended quadratic-residue codes

The first one below is special, thereafter all others are ordered by increasing A-numbers.

A120373 Weight distribution of [72,36,16] doubly-even binary self-dual extended quadratic-residue (or QR) code.

1, 0, 0, 2982, 214065, 18303516, 462306915, 4398818490, 16600354155, 25759476488, 16600354155, 4398818490, 462306915, 18303516, 214065, 2982, 0, 0, 1

A084554 Weight distribution of [104,52,20] binary extended quadratic-residue (or QR) code.

1, 0, 0, 0, 0, 1138150, 206232780, 15909698064, 567725836990, 9915185041320, 88355709788905, 413543821457520, 1036378989344140, 1406044530294756, 1036378989344140, 413543821457520, 88355709788905, 9915185041320

A097937 Weight distribution of [138,69,22] binary extended quadratic-residue (or QR) code.

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 321402, 2356948, 21533934, 490138050, 6648307504, 77865259035, 771068968365, 6551964560395, 48016671847203, 304734017875437, 1682222779056949, 8108674129521168

A098786 Weight distribution of [90,45,18] binary extended quadratic-residue (or QR) code.

1, 0, 0, 0, 0, 0, 0, 0, 0, 274120, 2819520, 30530115, 249109665, 1650476520, 8806726665, 38261417997, 136522171665, 402352364565, 983530112015, 2001805012350, 3403264592178, 4842229755990, 5773480681050

A142708 Weight distribution of [114,57,16] binary extended quadratic-residue (or QR) code.

1, 0, 0, 0, 0, 0, 0, 0, 25764, 0, 450870, 2795394, 36685789, 468994974, 4741799790, 40222705272, 282354497019, 1670741392215, 8378734842802, 35791510616904, 130792381305999, 410299386601373, 1108537936510704

A145578 Weight distribution of [18,9,6] binary extended quadratic-residue (or QR) code.

1, 0, 0, 102, 153, 153, 102, 0, 0, 1

A145648 Weight distribution of [42,21,10] binary extended quadratic-residue (or QR) code.

1, 0, 0, 0, 0, 1722, 10619, 49815, 157563, 341530, 487326, 487326, 341530, 157563, 49815, 10619, 1722, 0, 0, 0, 0, 1

A145657 Weight distribution of [74,37,14] binary extended quadratic-residue (or QR) code.

1, 0, 0, 0, 0, 0, 0, 8103, 89133, 1093905, 8481140, 53285328, 254815041, 961185963, 2871214319, 6824006274, 13019584383, 19988042838, 24737670308, 24737670308, 19988042838, 13019584383, 6824006274

A145659 Weight distribution of [80,40,16] binary extended quadratic-residue (or QR) code.

1, 0, 0, 0, 97565, 12882688, 590073120, 10588174080, 79707678050, 263303738880, 391106339008, 263303738880, 79707678050, 10588174080, 590073120, 12882688, 97565, 0, 0, 0, 1

A145683 Weight distribution of [98,49,16] binary extended quadratic-residue (or QR) code.

1, 0, 0, 0, 0, 0, 0, 0, 28518, 80801, 931588, 15038492, 166982396, 1358454930, 9150616832, 50926874040, 233809599765, 894066458642, 2860927585152, 7695094033816, 17462837266490, 33526663755928, 54576674050892

A145685 Weight distribution of [120,60,20] binary extended quadratic-residue (or QR) code.

1, 0, 0, 0, 0, 56896, 12886944, 2935906752, 320496430380, 18071400219840, 552526728803616, 9491105395362624, 94116098389459776, 549827720843995776, 1920594821540759296, 4051982879111857664

A145686 Weight distribution of [152,76,20] binary extended quadratic-residue (or QR) code.

1, 0, 0, 0, 0, 28690, 717250, 164250250, 39390351505, 5498418962110, 430930711621830, 19714914846904500, 542987434093298560, 9222363801696269312, 98458872937331752960, 670740325520798121984

A145687 Weight distribution of [168,84,24] binary extended quadratic-residue (or QR) code.

1, 0, 0, 0, 0, 0, 776216, 18130188, 5550332508, 1251282702264, 166071600559137, 13047136918828740, 629048543890724224, 19087130695796613120, 372099690249351069696, 4739291519495550533632

ternary quadratic-residue codes

A001382 Weight distribution of ternary [ 24,12,9 ] quadratic residue code (also of Pless symmetry code).

1, 0, 0, 4048, 61824, 242880, 198352, 24288, 48

A112641 Weight distribution of quadratic residue code of length 23 over GF(3).

1, 0, 0, 0, 0, 0, 0, 0, 1518, 2530, 0, 30912, 30912, 0, 151800, 91080, 0, 148764, 49588, 0, 21252, 3036, 0, 48

Other codes named K...P

Nordstrom-Robinson codes

A010032 Weight distribution of binary (16,256,6) nonlinear Nordstrom-Robinson code.

1, 0, 0, 112, 30, 112, 0, 0, 1

Preparata codes

A028239 Weight distribution of (64,2^52,6) Preparata code.

1, 0, 0, 41664, 2118168, 74203584, 1602647424, 23369897088, 238532662620, 1758643689600, 9579950593920, 39232098538560, 122387418032040, 293729091759936, 546275088069376, 791155554970368, 894836772921798

A028241 Weight distribution of (256,2^240,6) Preparata code.

1, 0, 0, 11606784, 12488692320, 8509435758336, 3885171732897280, 1265714256525580800, 307579088363780015856, 57656001868130930526720, 8558274844383035735717376, 1027363469418768308971019520

Kerdock codes

A028238 Weight distribution of (64,4096,28) Kerdock code.

1, 0, 0, 0, 0, 0, 0, 1984, 126, 1984, 0, 0, 0, 0, 0, 0, 1

A028240 Weight distribution of (256,2^16,120) Kerdock code.

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 32512, 510, 32512, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1

(check out A028239)

Hoffman-Singleton and Higman-Sims graph related

A015064 Weight distribution of [50,21,12] code associated with Hoffman-Singleton and Higman-Sims graphs.

1, 0, 0, 0, 0, 0, 1050, 925, 21875, 68250, 169925, 333300, 453250, 453250, 333300, 169925, 68250, 21875, 925, 1050, 0, 0, 0, 0, 0, 1

A015065 Weight distribution of [50,29,8] code associated with Hoffman-Singleton and Higman-Sims graphs.

1, 0, 0, 0, 800, 8295, 114625, 920175, 4627875, 17257800, 45069885, 84369875, 116066125, 116066125, 84369875, 45069885, 17257800, 4627875, 920175, 114625, 8295, 800, 0, 0, 0, 1

A015066 Weight distribution of [50,22,7] code associated with Hoffman-Singleton and Higman-Sims graphs.

1, 0, 0, 0, 0, 0, 0, 50, 0, 0, 0, 0, 1050, 0, 925, 12700, 21875, 34300, 68250, 107800, 169925, 258000, 333300, 404250, 453250, 462952, 453250, 404250, 333300, 258000, 169925, 107800, 68250, 34300, 21875, 12700, 925, 0, 1050, 0, 0, 0, 0, 50, 0, 0, 0, 0, 0, 0, 1

A015067 Weight distribution of [50,28,8] code associated with Hoffman-Singleton and Higman-Sims graphs.

1, 0, 0, 0, 750, 7770, 52675, 449550, 2311575, 8624700, 22661835, 42102850, 57811425, 58254700, 42267025, 22408050, 8633100, 2316300, 470625, 61950, 525, 50, 0, 0, 0, 1

A015068 Weight distribution of [100,22,22] code associated with Hoffman-Singleton and Higman-Sims graphs.

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 100, 0, 0, 0, 1100, 3850, 0, 4125, 38500, 92400, 193600, 347600, 485100, 600600, 660352, 600600, 485100, 347600, 193600, 92400, 38500, 4125, 0, 3850, 1100, 0, 0, 0, 100, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1

A015069 Weight distribution of [100,78,6] code associated with Hoffman-Singleton and Higman-Sims graphs.

1, 0, 0, 3850, 0, 8625540, 504741475, 21060732550, 641604305375, 14622264133400, 255578801503795, 3496197414021950, 38040184865580975, 333583288959605300, 2383620258950558925, 14005822677643540370, 68193674451079227050, 276907651030419444000, 942804612331379390725, 2703690041528811696900, 6554715235199646035290, 13474850115575617584200, 23545377618939915393150, 35033702002644035359900, 44444350668327576562750, 48108741996656177342352

A015070 Weight distribution of [100,22,32] code associated with Hoffman-Singleton and Higman-Sims graphs.

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3850, 5600, 4125, 0, 92400, 387200, 347600, 0, 600600, 1311552, 600600, 0, 347600, 387200, 92400, 0, 4125, 5600, 3850, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1

A015071 Weight distribution of [100,78,8] code associated with Hoffman-Singleton and Higman-Sims graphs.

1, 0, 0, 0, 137225, 7231840, 511741475, 20997046400, 642104180575, 14620696059200, 255580729090995, 3496191224323200, 38040223036760175, 333583215539666400, 2383620193904285325, 14005823013894187520, 68193674589734420650, 276907649362395385600, 942804613467381809925, 2703690046024936460800, 6554715226694274576090, 13474850114631510264000, 23545377636355278743550, 35033701987289528723200, 44444350658167367673150, 48108742023087188141952

Hamming codes

A002337 Weight distribution of [8,4,4] Hamming code.

1, 0, 0, 0, 14, 0, 0, 0, 1

A002393 Weight distribution of [8,4,4] Hamming code.

1, 14, 1

A002394 Weight distribution of [ 7,4,3 ] Hamming code.

1, 0, 0, 7, 7, 0, 0, 1

A010085 Weight distribution of [15,11,3] Hamming code of length 15 and minimal distance 3.

1, 0, 0, 35, 105, 168, 280, 435, 435, 280, 168, 105, 35, 0, 0, 1

A010086 Weight distribution of d=3 Hamming code of length 31.

1, 0, 0, 155, 1085, 5208, 22568, 82615, 247845, 628680, 1383096, 2648919, 4414865, 6440560, 8280720, 9398115, 9398115, 8280720, 6440560, 4414865, 2648919, 1383096, 628680, 247845, 82615, 22568

A010087 Weight distribution of d=3 Hamming code of length 63.

1, 0, 0, 651, 9765, 109368, 1057224, 8649279, 60544953, 369776680, 1996794072, 9621890019, 41694856749, 163568562192, 584173436400, 1908310936455, 5724932809365, 15827726179440, 40448633569680

A010088 Weight distribution of d=3 Hamming code of length 127.

1, 0, 0, 2667, 82677, 1984248, 40346376, 698136399, 10472045985, 138455313640, 1633772700952, 17377481697723, 167982323077989, 1485996809606736, 12100259735369136, 91155294690805839

A010089 Weight distribution of [255,247,3] Hamming code of length 255.

1, 0, 0, 10795, 680085, 33732216, 1405509000, 50008107375, 1550251328625, 42545493649000, 1046619143765400, 23311068641056875, 473991729034823125, 8859999141328482000, 153151413728678046000

A010090 Weight distribution of d=4 Hamming code of length 15.

1, 0, 105, 280, 435, 168, 35

A010091 Weight distribution of d=4 Hamming code of length 31.

1, 0, 1085, 22568, 247845, 1383096, 4414865, 8280720, 9398115, 6440560, 2648919, 628680, 82615, 5208, 155

A010092 Weight distribution of d=4 Hamming code of length 63.

1, 0, 9765, 1057224, 60544953, 1996794072, 41694856749, 584173436400, 5724932809365, 40448633569680, 210758816714985, 823875120414360, 2447745309517725, 5580858785942664, 9832942289229633, 13449656041565856

A010093 Weight distribution of d=4 Hamming code of length 127.

1, 0, 82677, 40346376, 10472045985, 1633772700952, 167982323077989, 12100259735369136, 638087062835640873, 25460924781434105040, 788752649609653468509, 19363706818511194074168

A010095 Weight distribution of d=4 Hamming code of length 255.

1, 0, 680085, 1405509000, 1550251328625, 1046619143765400, 473991729034823125, 153151413728678046000, 36909490731397295108625, 6861064221248350742706000, 1009876431641919171349467525

Extended Hamming codes

A010080 Weight distribution of [16,11,4] extended Hamming code of length 16.

1, 0, 140, 448, 870, 448, 140, 0, 1

A010081 Weight distribution of extended Hamming code of length 32 (or 3rd order Reed-Muller code).

1, 0, 1240, 27776, 330460, 2011776, 7063784, 14721280, 18796230, 14721280, 7063784, 2011776, 330460, 27776, 1240, 0, 1

A010082 Weight distribution of extended Hamming code of length 64.

1, 0, 10416, 1166592, 69194232, 2366570752, 51316746768, 747741998592, 7633243745820, 56276359749120, 306558278858160, 1255428754917120, 3916392495228360, 9399341113166592, 17480786291963792

A010083 Weight distribution of [128,120,4] extended Hamming code of length 128. This is also the Reed-Muller code RM(5,7).

1, 0, 85344, 42330624, 11170182384, 1772228014592, 185359804775712, 13586256544975872, 729242357526446712, 29627257927486958592, 934817955092922629344, 23382589365749366429184

A010084 Weight distribution of extended Hamming code of length 256.

1, 0, 690880, 1439241216, 1600259436000, 1089164637414400, 497302797675880000, 162011412870006528000, 39370123446823781449200, 7379968237981419286272000, 1095459180086149609599422400

A105547 Hamming weight distribution of code obtained by lifting Golay code of length 24 to Z/4Z.

1, 0, 0, 0, 0, 0, 0, 0, 759, 0, 12144, 0, 172592, 61824, 765072, 1133440, 1239447, 4080384, 1445136, 4080384, 1870176, 1133440, 692208, 61824, 28385

Golay codes

A001380 Weight distribution of binary Golay code of length 24.

1, 0, 759, 2576, 759, 0, 1

A002289 Weight distribution of [ 23,12,7 ] binary perfect Golay code.

1, 0, 0, 0, 0, 0, 0, 253, 506, 0, 0, 1288, 1288, 0, 0, 506, 253, 0, 0, 0, 0, 0, 0, 1

A104336 Weight distribution of [24,12,8] binary Golay code.

1, 0, 0, 0, 0, 0, 0, 0, 759, 0, 0, 0, 2576, 0, 0, 0, 759, 0, 0, 0, 0, 0, 0, 0, 1

A105683 Weight distribution of [12,6,6]_3 ternary extended Golay code.

1, 0, 264, 440, 24

A105918 Weight distribution of [24,12,6] odd Golay code.

1, 0, 0, 64, 375, 960, 1296, 960, 375, 64, 0, 0, 1

A105684 Weight distribution of [11,6,5]_3 ternary Golay perfect code.

1, 0, 0, 0, 0, 132, 132, 0, 330, 110, 0, 24

A018235 Weight distribution of (48,2^24,12) binary code obtained from Golay code of length 24 lifted to Z/4Z and mapped to GF(2)^2.

1, 0, 0, 0, 0, 0, 12144, 61824, 195063, 1133440, 1445136, 4080384, 2921232, 4080384, 1445136, 1133440, 195063, 61824, 12144, 0, 0, 0, 0, 0, 1

Other ternary codes

A002521 Weight distribution of [ 28,14,9 ] ternary self-dual code.

1, 0, 0, 2184, 78624, 768096, 2159976, 1555632, 216216, 2240

A106056 Weight distribution of [13,6,6]_3 ternary code p_{13}.

1, 0, 156, 494, 78

double circulant codes

A002606 Weight distribution of Karlin's [ 28,14,8 ] double circulant code.

1, 0, 0, 0, 546, 1456, 3549, 5280, 3549, 1456, 546, 0, 0, 0, 1

A080477 Weight distribution of [120,60,20] double circulant code.

1, 0, 0, 0, 0, 71862, 38266515, 6114942900, 475562216745, 18824858869630, 397449398883096, 4630515150103920, 30531593455793640, 116023986363853264, 257257754706576192, 335200293307691456

A131353 Weight distribution of [124,62,20] double circulant code.

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 90768, 529480, 10873250, 171180884, 2159102198, 22668808776, 199576556020, 1489045613508, 9466389337938, 51549138453256, 241551099887720, 977979841051968, 3433274842143012

A146889 Weight distribution of [12,6,4] double circulant code.

1, 0, 15, 32, 15, 0, 1

A146893 Weight distribution of [40,20,8] double circulant code.

1, 0, 285, 21280, 239970, 525504, 239970, 21280, 285, 0, 1

A146894 Weight distribution of [60,30,12] double circulant code.

1, 0, 0, 4060, 24360, 294930, 1728400, 7758660, 26336640, 67403540, 129936240, 192974265, 220819632, 192974265, 129936240, 67403540, 26336640, 7758660, 1728400, 294930, 24360, 4060, 0, 0, 1

A146895 Weight distribution of [76,38,12] double circulant code.

1, 0, 0, 2109, 86469, 961704, 7489059, 53574224, 275509215, 1113906312, 3626095793, 9404812736, 19610283420, 33067534032, 45200010670, 50157375456, 45200010670, 33067534032, 19610283420, 9404812736

A146896 Weight distribution of [88,44,16] double circulant code.

1, 0, 0, 0, 32164, 6992832, 535731625, 16623384448, 225426781470, 1405590745152, 4163803131796, 5968212445440, 4163803131796, 1405590745152, 225426781470, 16623384448, 535731625, 6992832, 32164, 0, 0, 0, 1

A146897 Weight distribution of [108,54,20] double circulant code.

1, 0, 0, 0, 0, 260442, 5804136, 74455407, 746650008, 6776021115, 48988609776, 296249593887, 1505946930696, 6456853758147, 23472658198080, 72678166237737, 192293022909528, 436002802265628, 849260837522448

A146946 Weight distribution of [136,68,24] double circulant code.

1, 0, 0, 0, 0, 0, 3997890, 1228844320, 182985731775, 14283914414016, 612875802567105, 14997654299809440, 215365307912371904, 1855049119250976000, 9745212817192720384, 31607315976754470912

A146947 Weight distribution of [168,84,24] double circulant code.

1, 0, 0, 0, 0, 0, 571704, 17008194, 5507510484, 1252615755636, 166058829151929, 13047194638256310, 629048483051035008, 19087129808556584960, 372099697089030127616, 4739291490433882914816

BCH codes

binary BCH codes

A010463 Weight distribution of [32,21,6] BCH code.

1, 0, 0, 992, 10540, 60512, 228160, 446400, 603942, 446400, 228160, 60512, 10540, 992, 0, 0, 1

primitive binary BCH codes

A083488 Weight distribution of [127,99,9] primitive binary BCH code.

1, 0, 0, 0, 0, 0, 0, 0, 0, 62230, 734314, 8454390, 81725770, 706987918, 5756901618, 43470567491, 304293972437, 1986688064970, 12140871508150, 69649172729570, 376105532739678, 1916352155002274, 9233333110465502

A097479 Weight distribution of [127,50,27] primitive binary BCH code.

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 40894, 146050, 0, 0, 4853051, 14559153, 0, 0, 310454802, 793384494, 0, 0, 10538703840, 23185148448, 0, 0, 199123183160, 380144258760, 0, 0, 2154195406104

A111332 Weight distribution of [127,57,23] primitive binary BCH code.

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 112014, 485394, 0, 0, 5376672, 19202400, 0, 0, 609444171, 1828332513, 0, 0, 39831154272, 101790727584, 0, 0, 1348537052730, 2966781516006, 0, 0, 25489124479104

A151700 Weight distribution of [15,7,5] primitive binary BCH code.

1, 0, 0, 0, 0, 18, 30, 15, 15, 30, 18, 0, 0, 0, 0, 1

A151701 Weight distribution of [31,11,11] primitive binary BCH code.

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 186, 310, 0, 0, 527, 527, 0, 0, 310, 186, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1

A151713 Weight distribution of [63,10,27] primitive binary BCH code.

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 196, 252, 0, 0, 63, 63, 0, 0, 252, 196, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1

A151721 Weight distribution of [63,16,23] primitive binary BCH code.

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1890, 3150, 0, 0, 5488, 7056, 0, 0, 15183, 15183, 0, 0, 7056, 5488, 0, 0, 3150, 1890, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1

A151722 Weight distribution of [63,18,21] primitive binary BCH code.

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1452, 2772, 1890, 3150, 9828, 14364, 5488, 7056, 32760, 37128, 15183, 15183, 37128, 32760, 7056, 5488, 14364, 9828, 3150, 1890, 2772, 1452, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1

A151736 Weight distribution of [63,24,15] primitive binary BCH code.

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 651, 1953, 3024, 7728, 0, 0, 74448, 142128, 109368, 182280, 668304, 976752, 388864, 499968, 2071440, 2347632, 914067, 914067, 2347632, 2071440, 499968, 388864, 976752, 668304, 182280, 109368

A151769 Weight distribution of [63,30,13] primitive binary BCH code.

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1764, 6300, 7707, 23121, 177660, 454020, 352800, 776160, 4820112, 9202032, 5486040, 9143400, 42679728, 62378064, 28457632, 36588384, 132625080, 150308424, 53382483, 53382483, 150308424

A151770 Weight distribution of [63,36,11] primitive binary BCH code.

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5670, 24570, 77616, 277200, 895755, 2687265, 7623504, 19482288, 45331650, 99729630, 207320256, 395793216, 694879416, 1158132360, 1835136576, 2682122688, 3618111196, 4651857252, 5702931360

A151771 Weight distribution of [63,39,9] primitive binary BCH code.

1, 0, 0, 0, 0, 0, 0, 0, 0, 2170, 11718, 32382, 140322, 628866, 2245950, 7302603, 21907809, 60355638, 154242186, 365056650, 803124630, 1648195230, 3146554530, 5596735032, 9327891720, 14579965764, 21309180732

A151772 Weight distribution of [63,45,7] primitive binary BCH code.

1, 0, 0, 0, 0, 0, 0, 3411, 23877, 78400, 423360, 2388456, 10349976, 39912768, 142545600, 465744279, 1397232837, 3864176064, 9875116608, 23391438840, 51461165448, 105345653952, 201114430272, 358601331375, 597668885625

A151773 Weight distribution of [63,51,5] primitive binary BCH code.

1, 0, 0, 0, 0, 1890, 18270, 133443, 934101, 5789350, 31262490, 150280200, 651214200, 2556010044, 9128607300, 29816643927, 89449931781, 247309297956, 632012650332, 1496867946840, 3293109483048

A151810 Weight distribution of [127,15,55] primitive binary BCH code.

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3556, 4572, 0, 0, 0, 0, 0, 0, 8255, 8255, 0, 0, 0, 0, 0, 0, 4572, 3556, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0

A151811 Weight distribution of [127,22,47] primitive binary BCH code.

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16002, 26670, 0, 0, 0, 0, 0, 0, 384048, 493776, 0, 0, 0, 0, 0, 0, 1176655, 1176655, 0, 0, 0, 0, 0, 0, 493776, 384048, 0, 0, 0, 0, 0, 0

A151812 Weight distribution of [127,29,43] primitive binary BCH code.

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 128524, 245364, 0, 0, 954786, 1591310, 0, 0, 6518148, 9526524, 0, 0, 24678640, 31729680, 0, 0, 54726840, 62023752, 0, 0, 76311887

A151813 Weight distribution of [127,36,31] primitive binary BCH code.

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2667, 8001, 0, 0, 4572, 11684, 0, 0, 640080, 1408176, 0, 0, 12220956, 23330916, 0, 0, 132560568, 220934280, 0, 0, 823921644, 1204193172, 0, 0, 3157059472

A151815 Weight distribution of [127,43,31] primitive binary BCH code.

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 31115, 93345, 0, 0, 2478024, 6332728, 0, 0, 82356960, 181185312, 0, 0, 1554145736, 2967005496, 0, 0, 16837453752, 28062422920, 0, 0, 106485735720

A151818 Weight distribution of [127,64,21] primitive binary BCH code.

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 41910, 201930, 1285494, 5570474, 21935186, 86053422, 323695568, 1156055600, 3886222860, 12694994676, 40367970699, 121103912097, 343251594420, 948989702220

A151838 Weight distribution of [127,71,19] primitive binary BCH code.

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 417830, 2256282, 6442964, 31043372, 157443678, 682255938, 2808212316, 11016832932, 41125294686, 146876052450, 501584808360, 1638510373976, 5127674481867

A151839 Weight distribution of [127,78,15] primitive binary BCH code.

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 48387, 338709, 768096, 4693920, 33284160, 179734464, 912632160, 4397227680, 20128275720, 87222528120, 358733348064, 1407338519328, 5266329775168, 18808320625600

A151840 Weight distribution of [127,85,13] primitive binary BCH code.

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 37338, 304038, 2765171, 19356197, 120511062, 736456490, 4254825120, 22976055648, 116946815128, 563471018344, 2572832433192, 11148940543832, 45932301765896, 180195953081592

A151841 Weight distribution of [127,92,11] primitive binary BCH code.

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 112014, 1082802, 4992624, 40654224, 343960323, 2407722261, 15478798608, 94592658160, 544439184170, 2939971594518, 14970193795392, 72129115559616, 329317484468616, 1427042432697336

A151876 Weight distribution of [127,106,7] primitive binary BCH code.

1, 0, 0, 0, 0, 0, 0, 48387, 725805, 8249920, 97349056, 1065157128, 10296518904, 90631060800, 737995780800, 5564376646815, 38950636527705, 254287368764352, 1553978364671040, 8915151283570840

A151877 Weight distribution of [127,113,5] primitive binary BCH code.

1, 0, 0, 0, 0, 16002, 325374, 5455539, 81833085, 1081441830, 12761013594, 135766920744, 1312413567192, 11609278871820, 94532699384820, 712151423629407, 4985059965405849, 32549472610146324

A151878 Weight distribution of [255,37,91] primitive binary BCH code.

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 563040, 1003680, 0, 0, 2754306, 4590510, 0, 0, 22848000, 35642880, 0, 0, 125386560, 183257280, 0, 0, 501228000, 686868000

A151909 Weight distribution of [255,45,87] primitive binary BCH code.

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 10875920, 20763120, 0, 0, 85112880, 151722960, 0, 0, 839823426, 1399705710, 0, 0, 5839330000, 9109354800

A151933 Weight distribution of [255,47,85] primitive binary BCH code.

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8927058, 17646510, 10875920, 20763120, 73352790, 135295146, 85112880, 151722960

A151934 Weight distribution of [255,55,63] primitive binary BCH code.

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 10795, 32385, 35700, 94860, 293760, 750720, 3102840, 7080840, 7221600, 15887520

A151935 Weight distribution of [255,63,63] primitive binary BCH code.

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 10795, 32385, 67320, 193800, 410550, 1090890, 2074680, 5301960, 28493700

A151936 Weight distribution of [255,207,13] primitive binary BCH code.

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8721510, 150757530, 2251459107, 33771886605, 472011374250, 6241039281750, 77847220528800, 918597202239840, 10278084342056520, 109321442547328440, 1107488282649954120

A151937 Weight distribution of [255,215,11] primitive binary BCH code.

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 7152750, 145439250, 2134260240, 36892212720, 575741656947, 8636124854205, 120888835017840, 1598419040791440, 19927324013927850, 235142423364348630, 2631224344379928000

A151938 Weight distribution of [255,223,9] primitive binary BCH code.

1, 0, 0, 0, 0, 0, 0, 0, 0, 2586550, 63629130, 1389956550, 28262449850, 528075710190, 9128165847570, 146665445085747, 2199981676286205, 30929084994308490, 408951234924745590, 5101129401023536050

A151939 Weight distribution of [255,231,7] primitive binary BCH code.

1, 0, 0, 0, 0, 0, 0, 856035, 26537085, 645102400, 15869519040, 355776960840, 7234131537080, 135192235752000, 2336894360856000, 37546273785247407, 563194106778711105, 7917846995071200960, 104691532490385879360

A151940 Weight distribution of [255,239,5] primitive binary BCH code.

1, 0, 0, 0, 0, 134946, 5622750, 195214995, 6051664845, 166197204550, 4088451231930, 91058768160360, 1851528285927320, 34609373477200620, 598247741534467860, 9611846516874799215, 144177697753121988225

extended binary primitive BCH codes

A030639 Weight distribution of [128,43,32] extended binary primitive BCH (or XBCH) code.

1, 0, 0, 0, 0, 0, 0, 0, 124460, 8810752, 263542272, 4521151232, 44899876672, 262118734080, 915924097536, 1931974003456, 2476672341286, 1931974003456, 915924097536, 262118734080, 44899876672, 4521151232

A147628 Weight distribution of [64,10,28] extended binary primitive BCH (or XBCH) code.

1, 0, 0, 0, 0, 0, 0, 448, 126, 448, 0, 0, 0, 0, 0, 0, 1

A147632 Weight distribution of [64,16,24] extended binary primitive BCH (or XBCH) code.

1, 0, 0, 0, 0, 0, 5040, 12544, 30366, 12544, 5040, 0, 0, 0, 0, 0, 1

A147633 Weight distribution of [128,15,56] extended binary primitive BCH (or XBCH) code.

1, 0, 0, 0, 0, 0, 0, 8128, 16510, 8128, 0, 0, 0, 0, 0, 0, 1

A147635 Weight distribution of [128,22,48] extended binary primitive BCH (or XBCH) code.

1, 0, 0, 0, 0, 0, 42672, 877824, 2353310, 877824, 42672, 0, 0, 0, 0, 0, 1

A109488 Weight distribution of [64,18,22] extended binary primitive BCH (or XBCH) code.

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4224, 5040, 24192, 12544, 69888, 30366, 69888, 12544, 24192, 5040, 4224, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1

A147770 Weight distribution of [128,29,44] extended binary primitive BCH (or XBCH) code.

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 373888, 2546096, 16044672, 56408320, 116750592, 152623774, 116750592, 56408320, 16044672, 2546096, 373888, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1

A151411 Weight distribution of [128,36,32] extended binary primitive BCH (or XBCH) code.

1, 0, 0, 0, 0, 0, 0, 0, 10668, 16256, 2048256, 35551872, 353494848, 2028114816, 7216135936, 14981968512, 19484794406, 14981968512, 7216135936, 2028114816, 353494848, 35551872, 2048256, 16256, 10668, 0, 0, 0, 0, 0, 0, 0, 1

A140792 Weight distribution of [128,64,22] extended binary primitive BCH (or XBCH) code.

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 243840, 6855968, 107988608, 1479751168, 16581217536, 161471882796, 1292241296640, 9106516329984, 53383279307904, 278420690161824, 1218666847725184, 4782630191822848

A151422 Weight distribution of [128,50,28] extended binary primitive BCH (or XBCH) code.

1, 0, 0, 0, 0, 0, 0, 186944, 19412204, 1103839296, 33723852288, 579267441920, 5744521082944, 33558415333632, 117224663972352, 247312085243776, 316992306111910, 247312085243776, 117224663972352, 33558415333632

A151435 Weight distribution of [128,57,24] extended binary primitive BCH (or XBCH) code.

1, 0, 0, 0, 0, 0, 597408, 24579072, 2437776684, 141621881856, 4315318568736, 74150180302848, 735289205007168, 4295496356229120, 15004724612905792, 31655991621445632, 40574965317267238, 31655991621445632

A151513 Weight distribution of [128,71,20] extended binary primitive BCH (or XBCH) code.

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2674112, 37486336, 839699616, 13825045248, 188001347136, 2140095182336, 20510697927468, 166689980438016, 1156658661471040, 6886497209935616, 35363776220195360

A151559 Weight distribution of [128,85,14] extended binary primitive BCH (or XBCH) code.

1, 0, 0, 0, 0, 0, 0, 341376, 22121368, 856967552, 27230880768, 680417833472, 13721772977024, 226128254847488, 3081454360189952, 35064826913355520, 336014520825141340, 2731238665152128768, 18949612280501341184

A151560 Weight distribution of [128,92,12] extended binary primitive BCH (or XBCH) code.

1, 0, 0, 0, 0, 0, 1194816, 45646848, 2751682584, 110071456768, 3484410778688, 87099309355008, 1756359917165952, 28944450656120832, 394426389988237184, 4488297727663171584, 43009842715896693084

A151561 Weight distribution of [128,99,10] extended binary primitive BCH (or XBCH) code.

1, 0, 0, 0, 0, 796544, 90180160, 6463889536, 347764539928, 14127559573120, 445754705469248, 11149685265467776, 224811690627712384, 3704895377802191104, 50486556173121673600, 574502176730571255552

A151562 Weight distribution of [128,106,8] extended binary primitive BCH (or XBCH) code.

1, 0, 0, 0, 774192, 105598976, 11361676032, 828626841600, 44515013174520, 1808265733435392, 57056968214853376, 1427159096213901312, 28775892186952836240, 474226642406696116224, 6462279071735110418944

A151563 Weight distribution of [128,113,6] extended binary primitive BCH (or XBCH) code.

1, 0, 0, 341376, 87288624, 13842455424, 1448180487936, 106141978256640, 5697211389035256, 231462916338818304, 7303265469631124224, 182676478544670888576, 3683313800412335283600

A151564 Weight distribution of [256,13,120] extended binary primitive BCH (or XBCH) code.

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3840, 510, 3840, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1

A151618 Weight distribution of [256,21,112] extended binary primitive BCH (or XBCH) code.

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 168640, 373760, 1012350, 373760, 168640, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1

A151619 Weight distribution of [256,29,96] extended binary primitive BCH (or XBCH) code.

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 359856, 37361920, 113229824, 234967710, 113229824, 37361920, 359856, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1

A151620 Weight distribution of [256,37,92] extended binary primitive BCH (or XBCH) code.

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1566720, 7344816, 58490880, 308643840, 1188096000, 3727770880, 8903669760, 16687560704, 24073697280, 27525271710, 24073697280, 16687560704, 8903669760

A151621 Weight distribution of [256,45,88] extended binary primitive BCH (or XBCH) code.

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 31639040, 236835840, 2239529136, 14948684800, 77258749440, 307810693120, 951255133440, 2282992005120, 4259254518784, 6189970585600, 7012375340190

A151622 Weight distribution of [256,47,86] extended binary primitive BCH (or XBCH) code.

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 26573568, 31639040, 208647936, 236835840, 2378672640, 2239529136, 17829665280, 14948684800, 105426881280

A151623 Weight distribution of [256,55,64] extended binary primitive BCH (or XBCH) code.

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 43180, 0, 0, 130560, 1044480, 10183680, 23109120, 270781440, 319610880, 4518816768, 5955102720, 59945135616, 64479928320, 598790983680

A151660 Weight distribution of [256,63,64] extended binary primitive BCH (or XBCH) code.

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 43180, 261120, 0, 1501440, 7376640, 98572800, 172078080, 2851952640, 4852262400, 67242055680, 96309150720, 1166182422528, 1459521557760

A151695 Weight distribution of [256,207,14] extended binary primitive BCH (or XBCH) code.

1, 0, 0, 0, 0, 0, 0, 159479040, 36023345712, 6713050656000, 996444422768640, 119599526889384960, 11813208348266177280, 973987499253055749120, 67857073021007558686720, 4036793565003066065373696

A151696 Weight distribution of [256,215,12] extended binary primitive BCH (or XBCH) code.

1, 0, 0, 0, 0, 0, 152592000, 39026472960, 9211866511152, 1719307875809280, 255069747378276480, 30617883280057344000, 3024174483076543522560, 249340897041415947755520, 17371409537486044559307520

A151697 Weight distribution of [256,223,10] extended binary primitive BCH (or XBCH) code.

1, 0, 0, 0, 0, 66215680, 29652406400, 9656241557760, 2346647121371952, 439880319919054080, 65294456333101261440, 7838161222769040003840, 774188816874234585880320, 63831272413784249623288320

A151698 Weight distribution of [256,231,8] extended binary primitive BCH (or XBCH) code.

1, 0, 0, 0, 27393120, 16514621440, 7589908497920, 2472086596608000, 600740380563958512, 112609379485457080320, 16715380562421902753280, 2006569275819918529044480, 198192337104269951401589280

A151699 Weight distribution of [256,239,6] extended binary primitive BCH (or XBCH) code.

1, 0, 0, 5757696, 6246879840, 4254648436480, 1942587054087680, 632857115011668480, 153789544269996787440, 28828000933861770693120, 4279137422192146077365760, 513681734709283283653090560

other binary codes

A002617 Weight distribution of Cheng-Sloane [ 32,17,8 ] code.

1, 0, 0, 0, 908, 3328, 14784, 27392, 38246, 27392, 14784, 3328, 908, 0, 0, 0, 1

A010031 Weight distribution of any one of the five doubly-even binary [32,16,8] codes (quadratic residue, Reed-Muller, etc.).

1, 0, 620, 13888, 36518, 13888, 620, 0, 1

A014488 Weight distribution of [ 17,9,7 ] code over GF(4).

1, 0, 0, 0, 0, 0, 0, 1224, 1530, 10200, 8160, 51408, 25704, 85680, 24480, 45288, 5661, 2808

A085518 One of the three possible weight distributions for a [16,7,6] binary code.

1, 0, 0, 45, 41, 34, 6, 1, 0

A085519 One of the three possible weight distributions for a [16,7,6] binary code.

1, 0, 0, 44, 45, 28, 10, 0, 0

A014487 Weight distribution of [ 18,9,8 ] self-dual code over GF(4).

1, 0, 0, 0, 2754, 18360, 77112, 110160, 50949, 2808

A018236 Weight distribution of hypothetical [ 72,36,16 ] doubly-even binary self-dual code.

1, 0, 0, 0, 249849, 18106704, 462962955, 4397342400, 16602715899, 25756721120, 16602715899, 4397342400, 462962955, 18106704, 249849, 0, 0, 0, 1

A018237 Weight distribution of hypothetical [ 68,34,12 ] code derived from hypothetical [ 72,36,16 ] doubly-even self-dual code.

1, 0, 0, 0, 0, 0, 442, 14960, 174471, 1478048, 9546537, 46699952, 175078410, 509477760, 1160564636, 2081169376, 2949602799, 3312254400, 2949602799, 2081169376, 1160564636, 509477760, 175078410, 46699952, 9546537, 1478048, 174471, 442, 0, 0, 0, 0, 0, 0, 1

A028299 Weight distribution of the dodecacode, a [12,0,6] quantum-error-correcting code.

1, 0, 0, 396, 1485, 1980, 234

A030030 Weight distribution of nonlinear binary (36,2^18,8) code.

1, 0, 0, 0, 306, 1530, 10608, 28152, 54621, 71708, 54621, 28152, 10608, 1530, 306, 0, 0, 0, 1

A030061 Weight distribution of [ 17,8,8 ] code over GF(4).

1, 0, 0, 0, 1530, 8160, 25704, 24480, 5661

A030062 Weight distribution of [ 96,48,12 ] doubly-even self-dual "octern" code.

1, 0, 0, 248, 9672, 3219288, 369688144, 18640824768, 422091297303, 4552776690944, 24292916390448, 65726628219120, 91448124030784, 65726628219120, 24292916390448, 4552776690944, 422091297303

A030331 Weight distribution of hypothetical [ 24,12,10 ] trace-self-dual additive code over GF(4).

1, 0, 0, 0, 0, 18216, 156492, 1147608, 3736557, 6248088, 4399164, 1038312, 32778

A131620 Weight distribution of a certain binary linear code of length 56 defined by AES (or Rijndael) S-box.

1, 0, 8, 27, 55, 240, 701, 1909, 5753, 15747, 41138, 104762, 252664, 580609, 1274691, 2665295, 5315469, 10113564, 18353698, 31781680, 52486460, 82606895, 123821091, 176518711, 238906435, 306378988, 371328696, 423932616

References

• M. Terada, J. Asatani and T. Koumoto, "Weight Distribution": http://www.infsys.cne.okayama-u.ac.jp/~kusaka/wd/index.html (original page: http://web.archive.org/20070711194415/http://www.infsys.cne.okayama-u.ac.jp/~koumoto/wd/index.html)