New binary self-dual codes via a variation of the four-circulant construction

Joe Gildea; Abidin Kaya; Bahattin Yildiz

New binary self-dual codes via a variation of the four-circulant construction

Joe Gildea, Abidin Kaya, Bahattin Yildiz

Informatics, Computing, and Cyber Systems, School of

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

4 Scopus citations

Abstract

In this work, we provide a variation of the four-circulant construction for self-dual codes. By applying the constructions over the alphabets F₂, F₂ + uF₂, F₄ + uF₄, we were able to obtain extremal binary self-dual codes of lengths 40, 64 including new extremal binary self-dual codes of length 68. More precisely, 43 new extremal binary self-dual codes of length 68 with new parameters have been constructed.

Original language	English (US)
Pages (from-to)	213-226
Number of pages	14
Journal	Mathematical Communications
Volume	25
Issue number	2
State	Published - 2020

Keywords

Circulant matrices
Extremal self-dual codes
Gray maps

ASJC Scopus subject areas

Analysis
Algebra and Number Theory
Geometry and Topology
Applied Mathematics

Cite this

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title = "New binary self-dual codes via a variation of the four-circulant construction",

abstract = "In this work, we provide a variation of the four-circulant construction for self-dual codes. By applying the constructions over the alphabets F2, F2 + uF2, F4 + uF4, we were able to obtain extremal binary self-dual codes of lengths 40, 64 including new extremal binary self-dual codes of length 68. More precisely, 43 new extremal binary self-dual codes of length 68 with new parameters have been constructed.",

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author = "Joe Gildea and Abidin Kaya and Bahattin Yildiz",

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AU - Kaya, Abidin

AU - Yildiz, Bahattin

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N2 - In this work, we provide a variation of the four-circulant construction for self-dual codes. By applying the constructions over the alphabets F2, F2 + uF2, F4 + uF4, we were able to obtain extremal binary self-dual codes of lengths 40, 64 including new extremal binary self-dual codes of length 68. More precisely, 43 new extremal binary self-dual codes of length 68 with new parameters have been constructed.

AB - In this work, we provide a variation of the four-circulant construction for self-dual codes. By applying the constructions over the alphabets F2, F2 + uF2, F4 + uF4, we were able to obtain extremal binary self-dual codes of lengths 40, 64 including new extremal binary self-dual codes of length 68. More precisely, 43 new extremal binary self-dual codes of length 68 with new parameters have been constructed.

KW - Circulant matrices

KW - Extremal self-dual codes

KW - Gray maps

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ER -

New binary self-dual codes via a variation of the four-circulant construction

Abstract

Keywords

ASJC Scopus subject areas

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