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A075928 List of codewords in binary lexicode with Hamming distance 4 written as decimal numbers. 54


%S 0,15,51,60,85,90,102,105,150,153,165,170,195,204,240,255,771,780,816,

%T 831,854,857,869,874,917,922,934,937,960,975,1011,1020,1285,1290,1334,

%U 1337,1360,1375,1379,1388,1427,1436,1440,1455,1478,1481,1525

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

%C 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.

%C The code is linear and infinite.

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

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

%H J. H. Conway and N. J. A. Sloane, <a href="https://doi.org/10.1109/TIT.1986.1057187">Lexicographic codes: error-correcting codes from game theory</a>, IEEE Transactions on Information Theory, 32:337-348, 1986.

%H R. W. Hamming, <a href="https://signallake.com/innovation/hamming.pdf">Error Detecting and Error Correcting Codes</a>, Bell System Tech. J., Vol. 29, April, 1950, pp. 147-160.

%H Bob Jenkins, <a href="http://burtleburtle.net/bob/math/lexicode.html">Tables of Binary Lexicodes</a>

%H Ari Trachtenberg, <a href="http://ipsit.bu.edu/phdthesis_html/phdthesis_html.html">Error-Correcting Codes on Graphs: Lexicodes, Trellises and Factor Graphs</a>

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

%K nonn,easy,base

%O 0,2

%A Bob Jenkins (bob_jenkins(AT)burtleburtle.net)

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Last modified September 19 15:21 EDT 2019. Contains 327198 sequences. (Running on oeis4.)