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A076831 Triangle T(n,k) read by rows giving number of inequivalent binary linear [n,k] codes (n >= 0, 0 <= k <= n). 6
1, 1, 1, 1, 2, 1, 1, 3, 3, 1, 1, 4, 6, 4, 1, 1, 5, 10, 10, 5, 1, 1, 6, 16, 22, 16, 6, 1, 1, 7, 23, 43, 43, 23, 7, 1, 1, 8, 32, 77, 106, 77, 32, 8, 1, 1, 9, 43, 131, 240, 240, 131, 43, 9, 1, 1, 10, 56, 213, 516, 705, 516, 213, 56, 10, 1, 1, 11, 71, 333, 1060, 1988, 1988 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

"The familiar appearance of the first few rows [...] provides a good example of the perils of too hasty extrapolation in mathematics." - Slepian.

The difference between this triangle and the one for which it can be so easily mistaken is A250002. - Tilman Piesk, Nov 10 2014.

REFERENCES

H. Fripertinger and A. Kerber, in AAECC-11, Lect. Notes Comp. Sci. 948 (1995), 194-204.

D. Slepian, Some further theory of group codes. Bell System Tech. J. 39 1960 1219-1252.

M. Wild, Enumeration of binary and ternary matroids and other applications of the Brylawski-Lucas Theorem, Preprint Nr. 1693, Tech. Hochschule Darmstadt, 1994

LINKS

Table of n, a(n) for n=0..72.

H. Fripertinger, Isometry Classes of Codes

Kent E. Morrison, Integer Sequences and Matrices Over Finite Fields, Journal of Integer Sequences, Vol. 9 (2006), Article 06.2.1.

M. Wild, Consequences of the Brylawski-Lucas Theorem for binary matroids, European Journal of Combinatorics 17 (1996) 309-316.

M. Wild, The asymptotic number of inequivalent binary codes and nonisomorphic binary matroids, Finite Fields and their Applications 6 (2000) 192-202.

Index entries for sequences related to binary linear codes

EXAMPLE

     k    0   1   2   3    4    5    6    7    8   9  10  11        sum

   n

   0      1                                                           1

   1      1   1                                                       2

   2      1   2   1                                                   4

   3      1   3   3   1                                               8

   4      1   4   6   4    1                                         16

   5      1   5  10  10    5    1                                    32

   6      1   6  16  22   16    6    1                               68

   7      1   7  23  43   43   23    7    1                         148

   8      1   8  32  77  106   77   32    8    1                    342

   9      1   9  43 131  240  240  131   43    9   1                848

  10      1  10  56 213  516  705  516  213   56  10   1           2297

  11      1  11  71 333 1060 1988 1988 1060  333  71  11   1       6928

CROSSREFS

Cf. A022166, A006116, A076766 (row sums). A034356 gives same table but with k=0 column omitted.

Sequence in context: A108086 A130595 A108363 * A197061 A230861 A119724

Adjacent sequences:  A076828 A076829 A076830 * A076832 A076833 A076834

KEYWORD

nonn,tabl,nice

AUTHOR

N. J. A. Sloane, Nov 21 2002

STATUS

approved

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Last modified February 22 13:09 EST 2018. Contains 299454 sequences. (Running on oeis4.)