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%I #11 Nov 22 2019 03:39:16
%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.
%Y A194851 is a subsequence.
%K nonn,easy,base
%O 0,2
%A Bob Jenkins (bob_jenkins(AT)burtleburtle.net)
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