Constructing error-correcting binary codes using transitive permutation groups

Antti Laaksonen; Patric R.J. Östergård

doi:10.1016/j.dam.2017.08.022

Constructing error-correcting binary codes using transitive permutation groups

Antti Laaksonen^*, Patric R.J. Östergård

^*Corresponding author for this work

Information Theory

Research output: Contribution to journal › Article › Scientific › peer-review

4 Citations (Scopus)

Abstract

Transitive permutation groups are recurrent in the study of automorphism groups of combinatorial objects. For binary error-correcting codes, groups are here considered that act transitively on the pairs of coordinates and coordinate values. By considering such groups in an exhaustive manner and carrying out computer searches, the following new bounds are obtained on A2(n,d), the maximum size of a binary code of length n and minimum distance d: A2(17,3)≥5632, A2(20,3)≥40960, A2(21,3)≥81920, A2(22,3)≥163840, A2(23,3)≥327680, A2(23,9)≥136, and A2(24,5)≥17920.

Original language	English
Pages (from-to)	65-70
Journal	Discrete Applied Mathematics
Volume	233
DOIs	https://doi.org/10.1016/j.dam.2017.08.022
Publication status	Published - 2017
MoE publication type	A1 Journal article-refereed

Keywords

Binary codes
Cliques
Error-correcting codes
Transitive groups

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10.1016/j.dam.2017.08.022

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title = "Constructing error-correcting binary codes using transitive permutation groups",

abstract = "Transitive permutation groups are recurrent in the study of automorphism groups of combinatorial objects. For binary error-correcting codes, groups are here considered that act transitively on the pairs of coordinates and coordinate values. By considering such groups in an exhaustive manner and carrying out computer searches, the following new bounds are obtained on A2(n,d), the maximum size of a binary code of length n and minimum distance d: A2(17,3)≥5632, A2(20,3)≥40960, A2(21,3)≥81920, A2(22,3)≥163840, A2(23,3)≥327680, A2(23,9)≥136, and A2(24,5)≥17920.",

keywords = "Binary codes, Cliques, Error-correcting codes, Transitive groups",

author = "Antti Laaksonen and {\"O}sterg{\aa}rd, {Patric R.J.}",

year = "2017",

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language = "English",

volume = "233",

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journal = "Discrete Applied Mathematics",

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T1 - Constructing error-correcting binary codes using transitive permutation groups

AU - Laaksonen, Antti

AU - Östergård, Patric R.J.

PY - 2017

Y1 - 2017

N2 - Transitive permutation groups are recurrent in the study of automorphism groups of combinatorial objects. For binary error-correcting codes, groups are here considered that act transitively on the pairs of coordinates and coordinate values. By considering such groups in an exhaustive manner and carrying out computer searches, the following new bounds are obtained on A2(n,d), the maximum size of a binary code of length n and minimum distance d: A2(17,3)≥5632, A2(20,3)≥40960, A2(21,3)≥81920, A2(22,3)≥163840, A2(23,3)≥327680, A2(23,9)≥136, and A2(24,5)≥17920.

AB - Transitive permutation groups are recurrent in the study of automorphism groups of combinatorial objects. For binary error-correcting codes, groups are here considered that act transitively on the pairs of coordinates and coordinate values. By considering such groups in an exhaustive manner and carrying out computer searches, the following new bounds are obtained on A2(n,d), the maximum size of a binary code of length n and minimum distance d: A2(17,3)≥5632, A2(20,3)≥40960, A2(21,3)≥81920, A2(22,3)≥163840, A2(23,3)≥327680, A2(23,9)≥136, and A2(24,5)≥17920.

KW - Binary codes

KW - Cliques

KW - Error-correcting codes

KW - Transitive groups

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DO - 10.1016/j.dam.2017.08.022

M3 - Article

AN - SCOPUS:85030458329

SN - 0166-218X

VL - 233

SP - 65

EP - 70

JO - Discrete Applied Mathematics

JF - Discrete Applied Mathematics

ER -

Constructing error-correcting binary codes using transitive permutation groups

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Keywords

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