A075926 List of codewords in binary lexicode with Hamming distance 3 written as decimal numbers.

0, 7, 25, 30, 42, 45, 51, 52, 75, 76, 82, 85, 97, 102, 120, 127, 385, 390, 408, 415, 427, 428, 434, 437, 458, 461, 467, 468, 480, 487, 505, 510, 642, 645, 667, 668, 680, 687, 689, 694, 713, 718, 720, 727, 739, 740, 762, 765, 771, 772, 794, 797, 809

Offset

0,2

Comments

This is also the (infinite) d=3 Hamming code.

Links

Rémy Sigrist, Table of n, a(n) for n = 0..8191

J. H. Conway and N. J. A. Sloane, Lexicographic codes: error-correcting codes from game theory, IEEE Transactions on Information Theory, 32:337-348, 1986.

R. W. Hamming, Error Detecting and Error Correcting Codes, Bell System Tech. J., Vol. 29, April, 1950, pp. 147-160.

Ari Trachtenberg, Error-Correcting Codes on Graphs: Lexicodes, Trellises and Factor Graphs

Crossrefs

Cf. A075928, A075929, A075930, A075927, A057716, A075931.

Sequence in context: A196013 A272366 A327107 * A368532 A065660 A100496

Adjacent sequences: A075923 A075924 A075925 * A075927 A075928 A075929

Keyword

nonn,easy,base

Author

Bob Jenkins (bob_jenkins(AT)burtleburtle.net)

Status

approved