The sextuply shortened binary Golay code is optimal

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openAccess

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Journal Title

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Volume Title

A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä

Date

2019-03-15

Major/Subject

Mcode

Degree programme

Language

en

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Series

Designs, Codes, and Cryptography

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.

Description

Keywords

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

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Citation

Östergård, P R J 2019, ' The sextuply shortened binary Golay code is optimal ', Designs Codes and Cryptography, vol. 87, no. 2-3, pp. 341–347 . https://doi.org/10.1007/s10623-018-0532-z