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A075928
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List of codewords in binary lexicode with Hamming distance 4 written as decimal numbers.
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54
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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
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,2
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COMMENTS
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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.
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REFERENCES
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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.
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LINKS
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Table of n, a(n) for n=0..46.
Bob Jenkins, Tables of Binary Lexicodes
Ari Trachtenberg, Error-Correcting Codes on Graphs: Lexicodes, Trellises and Factor Graphs
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CROSSREFS
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Cf. A075929, A075930, A075926, A075934, A075944, A075945, A075946, A075937, A075949, etc.
Sequence in context: A191746 A029941 A194851 * A020214 A127643 A227129
Adjacent sequences: A075925 A075926 A075927 * A075929 A075930 A075931
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KEYWORD
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nonn,easy
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AUTHOR
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Bob Jenkins (bob_jenkins(AT)burtleburtle.net)
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STATUS
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approved
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