The sextuply shortened binary Golay code is optimal

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Abstract

The maximum size of unrestricted binary three-error-correcting codes has been known up to the length of the binary Golay code, with two exceptions. Specifically, denoting the maximum size of an unrestricted binary code of length n and minimum distance d by A(n, d), it has been known that 64 ≤ A(18 , 8 ) ≤ 68 and 128 ≤ A(19 , 8 ) ≤ 131. In the current computer-aided study, it is shown that A(18 , 8 ) = 64 and A(19 , 8 ) = 128 , so an optimal code is obtained even after shortening the extended binary Golay code six times.

Details

Original languageEnglish
Pages (from-to)341–347
Number of pages7
JournalDesigns, Codes and Cryptography
Volume87
Issue number2-3
Early online date13 Aug 2018
Publication statusPublished - 15 Mar 2019
MoE publication typeA1 Journal article-refereed

    Research areas

  • Classification, Clique, Double counting, Error-correcting code, Golay code, UPPER-BOUNDS, UNRESTRICTED CODES, ERROR-CORRECTING CODES

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