

A075928


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


54



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
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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 alreadychosen 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.


REFERENCES

J. H. Conway and N. J. A. Sloane, Lexicographic codes: errorcorrecting codes from game theory, IEEE Transactions on Information Theory, 32:337348, 1986.
R. W. Hamming, Error Detecting and Error Correcting Codes, Bell System Tech. J., Vol. 29, April, 1950, pp. 147160.


LINKS

Table of n, a(n) for n=0..46.
Bob Jenkins, Tables of Binary Lexicodes
Ari Trachtenberg, ErrorCorrecting Codes on Graphs: Lexicodes, Trellises and Factor Graphs


CROSSREFS

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


KEYWORD

nonn,easy,base


AUTHOR

Bob Jenkins (bob_jenkins(AT)burtleburtle.net)


STATUS

approved



