Bordered constructions of self-dual codes from group rings and new extremal binary self-dual codes

Steven T. Dougherty; Joseph Gildea; Adrian Korban; Abidin Kaya; Alexander Tylyshchak; Bahattin Yildiz

doi:10.1016/j.ffa.2019.02.004

Bordered constructions of self-dual codes from group rings and new extremal binary self-dual codes

Steven T. Dougherty, Joseph Gildea, Adrian Korban, Abidin Kaya, Alexander Tylyshchak, Bahattin Yildiz

Informatics, Computing, and Cyber Systems, School of

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

22 Scopus citations

Abstract

We introduce a bordered construction over group rings for self-dual codes. We apply the constructions over the binary field and the ring F ₂ +uF ₂ , using groups of orders 9, 15, 21, 25, 27, 33 and 35 to find extremal binary self-dual codes of lengths 20, 32, 40, 44, 52, 56, 64, 68, 88 and best known binary self-dual codes of length 72. In particular we obtain 41 new binary extremal self-dual codes of length 68 from groups of orders 15 and 33 using neighboring and extensions. All the numerical results are tabulated throughout the paper.

Original language	English (US)
Pages (from-to)	108-127
Number of pages	20
Journal	Finite Fields and Their Applications
Volume	57
DOIs	https://doi.org/10.1016/j.ffa.2019.02.004
State	Published - May 2019

Keywords

Bordered constructions
Codes over rings
Extremal codes
Group rings
Self-dual codes

ASJC Scopus subject areas

Theoretical Computer Science
Algebra and Number Theory
General Engineering
Applied Mathematics

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10.1016/j.ffa.2019.02.004

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title = "Bordered constructions of self-dual codes from group rings and new extremal binary self-dual codes",

abstract = " We introduce a bordered construction over group rings for self-dual codes. We apply the constructions over the binary field and the ring F 2 +uF 2 , using groups of orders 9, 15, 21, 25, 27, 33 and 35 to find extremal binary self-dual codes of lengths 20, 32, 40, 44, 52, 56, 64, 68, 88 and best known binary self-dual codes of length 72. In particular we obtain 41 new binary extremal self-dual codes of length 68 from groups of orders 15 and 33 using neighboring and extensions. All the numerical results are tabulated throughout the paper.",

keywords = "Bordered constructions, Codes over rings, Extremal codes, Group rings, Self-dual codes",

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doi = "10.1016/j.ffa.2019.02.004",

language = "English (US)",

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T1 - Bordered constructions of self-dual codes from group rings and new extremal binary self-dual codes

AU - Dougherty, Steven T.

AU - Gildea, Joseph

AU - Korban, Adrian

AU - Kaya, Abidin

AU - Tylyshchak, Alexander

AU - Yildiz, Bahattin

PY - 2019/5

Y1 - 2019/5

N2 - We introduce a bordered construction over group rings for self-dual codes. We apply the constructions over the binary field and the ring F 2 +uF 2 , using groups of orders 9, 15, 21, 25, 27, 33 and 35 to find extremal binary self-dual codes of lengths 20, 32, 40, 44, 52, 56, 64, 68, 88 and best known binary self-dual codes of length 72. In particular we obtain 41 new binary extremal self-dual codes of length 68 from groups of orders 15 and 33 using neighboring and extensions. All the numerical results are tabulated throughout the paper.

AB - We introduce a bordered construction over group rings for self-dual codes. We apply the constructions over the binary field and the ring F 2 +uF 2 , using groups of orders 9, 15, 21, 25, 27, 33 and 35 to find extremal binary self-dual codes of lengths 20, 32, 40, 44, 52, 56, 64, 68, 88 and best known binary self-dual codes of length 72. In particular we obtain 41 new binary extremal self-dual codes of length 68 from groups of orders 15 and 33 using neighboring and extensions. All the numerical results are tabulated throughout the paper.

KW - Bordered constructions

KW - Codes over rings

KW - Extremal codes

KW - Group rings

KW - Self-dual codes

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SN - 1071-5797

VL - 57

SP - 108

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JO - Finite Fields and Their Applications

JF - Finite Fields and Their Applications

ER -

Bordered constructions of self-dual codes from group rings and new extremal binary self-dual codes

Abstract

Keywords

ASJC Scopus subject areas

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