A075928 List of codewords in binary lexicode with Hamming distance 4 written as decimal numbers.

0, 15, 51, 60, 85, 90, 102, 105, 150, 153, 165, 170, 195, 204, 240, 255, 771, 780, 816, 831, 854, 857, 869, 874, 917, 922, 934, 937, 960, 975, 1011, 1020, 1285, 1290, 1334, 1337, 1360, 1375, 1379, 1388, 1427, 1436, 1440, 1455, 1478, 1481, 1525

Offset

0,2

Comments

The lexicode of Hamming distance d is constructed greedily by stepping through the binary vectors in lexicographic order and accepting a vector if it is at Hamming distance at least d from all already-chosen vectors.

The code is linear and infinite.

This is also the (infinite) d=4 Hamming code.

Lexicodes with even Hamming distance can be constructed from the preceding lexicode of odd Hamming distance by prepending a single parity bit.

Links

Table of n, a(n) for n=0..46.

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.

Bob Jenkins, Tables of Binary Lexicodes

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

Crossrefs

Cf. A075929, A075930, A075926, A075934, A075944, A075945, A075946, A075937, A075949, etc.

A194851 is a subsequence.

Sequence in context: A349817 A278909 A194851 * A020214 A127643 A227129

Adjacent sequences: A075925 A075926 A075927 * A075929 A075930 A075931

Keyword

nonn,easy,base

Author

Bob Jenkins (bob_jenkins(AT)burtleburtle.net)

Status

approved