A075927 -id:A075927 - cp's OEIS frontend

A075926 List of codewords in binary lexicode with Hamming distance 3 written as decimal numbers.

0, 7, 25, 30, 42, 45, 51, 52, 75, 76, 82, 85, 97, 102, 120, 127, 385, 390, 408, 415, 427, 428, 434, 437, 458, 461, 467, 468, 480, 487, 505, 510, 642, 645, 667, 668, 680, 687, 689, 694, 713, 718, 720, 727, 739, 740, 762, 765, 771, 772, 794, 797, 809

Offset: 0

Bob Jenkins (bob_jenkins(AT)burtleburtle.net)

This is also the (infinite) d=3 Hamming code.

Rémy Sigrist, Table of n, a(n) for n = 0..8191
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.
Ari Trachtenberg, Error-Correcting Codes on Graphs: Lexicodes, Trellises and Factor Graphs

Cf. A075928, A075929, A075930, A075927, A057716, A075931.

A075932 Basis for code in A075931.

Original entry on oeis.org

31, 227, 805, 1354, 6182, 10315, 18731, 35149, 67943, 393255, 655433, 1181959, 6291497, 10485837, 18874658, 35653635, 69337155, 136446255, 270666054, 1610612779, 2684354638, 4831838504, 9126807585, 17716871269, 34896740609

Offset: 0

Bob Jenkins (bob_jenkins(AT)burtleburtle.net)

nonn

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.

Bob Jenkins, Tables of Binary Lexicodes
Ari Trachtenberg, Error-Correcting Codes on Graphs: Lexicodes, Trellises and Factor Graphs

Cf. A075928, A075929, A075930, A075931, A075933, A075935, A075927, A075938.

a(n) = b(2^n), where b is A075931, the binary lexicode, d=5.

b(n) = XOR(a(i)) for all i where the i-th bit is set in n.

cp's OEIS Frontend

A075926 List of codewords in binary lexicode with Hamming distance 3 written as decimal numbers.

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