New extremal binary self-dual codes of length 68 from R2-lifts of binary self-dual codes

Suat Karadeniz; Bahattin Yildiz

doi:10.3934/amc.2013.7.219

New extremal binary self-dual codes of length 68 from R₂-lifts of binary self-dual codes

Suat Karadeniz, Bahattin Yildiz

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

7 Scopus citations

Abstract

A lift of binary self-dual codes to the ring R₂ is described. By using this lift, a family of self-dual codes over R₂ of length 17 are constructed. Taking the binary images of these codes, extremal binary self-dual codes of length 68 are obtained. For the first time in the literature, extremal binary codes of length 68 with γ = 4 and γ = 6 in W_68,2 have been obtained. In addition to these, six new codes with γ = 0 and fourteen new codes with γ = 2 in W_68,2 have also been found.

Original language	English (US)
Pages (from-to)	219-229
Number of pages	11
Journal	Advances in Mathematics of Communications
Volume	7
Issue number	2
DOIs	https://doi.org/10.3934/amc.2013.7.219
State	Published - May 2013
Externally published	Yes

Keywords

Codes over rings
Extremal codes
Gray map
Self-dual codes

ASJC Scopus subject areas

Algebra and Number Theory
Computer Networks and Communications
Discrete Mathematics and Combinatorics
Applied Mathematics

Access to Document

10.3934/amc.2013.7.219

Cite this

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title = "New extremal binary self-dual codes of length 68 from R2-lifts of binary self-dual codes",

abstract = "A lift of binary self-dual codes to the ring R2 is described. By using this lift, a family of self-dual codes over R2 of length 17 are constructed. Taking the binary images of these codes, extremal binary self-dual codes of length 68 are obtained. For the first time in the literature, extremal binary codes of length 68 with γ = 4 and γ = 6 in W68,2 have been obtained. In addition to these, six new codes with γ = 0 and fourteen new codes with γ = 2 in W68,2 have also been found.",

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N2 - A lift of binary self-dual codes to the ring R2 is described. By using this lift, a family of self-dual codes over R2 of length 17 are constructed. Taking the binary images of these codes, extremal binary self-dual codes of length 68 are obtained. For the first time in the literature, extremal binary codes of length 68 with γ = 4 and γ = 6 in W68,2 have been obtained. In addition to these, six new codes with γ = 0 and fourteen new codes with γ = 2 in W68,2 have also been found.

AB - A lift of binary self-dual codes to the ring R2 is described. By using this lift, a family of self-dual codes over R2 of length 17 are constructed. Taking the binary images of these codes, extremal binary self-dual codes of length 68 are obtained. For the first time in the literature, extremal binary codes of length 68 with γ = 4 and γ = 6 in W68,2 have been obtained. In addition to these, six new codes with γ = 0 and fourteen new codes with γ = 2 in W68,2 have also been found.

KW - Codes over rings

KW - Extremal codes

KW - Gray map

KW - Self-dual codes

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