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

Author

Bob Jenkins (bob_jenkins(AT)burtleburtle.net)

Keywords

• nonn
• easy
• base

Comments

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

Links

• 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

Crossrefs

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