The sextuply shortened binary Golay code is optimal

Patric R.J. Östergård*

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

1 Citation (Scopus)
69 Downloads (Pure)

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.

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

Keywords

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

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  • Projects

    Construction and Classification of Discrete Mathematic Structures

    Kokkala, J., Laaksonen, A., Heinlein, D., Ganzhinov, M., Östergård, P. & Szollosi, F.

    01/09/201524/09/2019

    Project: Academy of Finland: Other research funding

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