New extremal binary self-dual codes from block circulant matrices and block quadratic residue circulant matrices

J. Gildea; A. Kaya; R. Taylor; A. Tylyshchak; B. Yildiz

doi:10.1016/j.disc.2021.112590

New extremal binary self-dual codes from block circulant matrices and block quadratic residue circulant matrices

J. Gildea, A. Kaya, R. Taylor, A. Tylyshchak, B. Yildiz

Informatics, Computing, and Cyber Systems, School of

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

2 Scopus citations

Abstract

In this paper, we construct self-dual codes from a construction that involves both block circulant matrices and block quadratic residue circulant matrices. We provide conditions when this construction can yield self-dual codes. We construct self-dual codes of various lengths over F₂ and F₂+uF₂. Using extensions, neighbours and sequences of neighbours, we construct many new self-dual codes. In particular, we construct one new self-dual code of length 66 and 51 new self-dual codes of length 68.

Original language	English (US)
Article number	112590
Journal	Discrete Mathematics
Volume	344
Issue number	11
DOIs	https://doi.org/10.1016/j.disc.2021.112590
State	Published - Nov 2021

Keywords

Codes over rings
Quadratic double circulant codes
Self-dual codes

ASJC Scopus subject areas

Theoretical Computer Science
Discrete Mathematics and Combinatorics

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10.1016/j.disc.2021.112590

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title = "New extremal binary self-dual codes from block circulant matrices and block quadratic residue circulant matrices",

abstract = "In this paper, we construct self-dual codes from a construction that involves both block circulant matrices and block quadratic residue circulant matrices. We provide conditions when this construction can yield self-dual codes. We construct self-dual codes of various lengths over F2 and F2+uF2. Using extensions, neighbours and sequences of neighbours, we construct many new self-dual codes. In particular, we construct one new self-dual code of length 66 and 51 new self-dual codes of length 68.",

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author = "J. Gildea and A. Kaya and R. Taylor and A. Tylyshchak and B. Yildiz",

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AU - Gildea, J.

AU - Kaya, A.

AU - Taylor, R.

AU - Tylyshchak, A.

AU - Yildiz, B.

PY - 2021/11

Y1 - 2021/11

N2 - In this paper, we construct self-dual codes from a construction that involves both block circulant matrices and block quadratic residue circulant matrices. We provide conditions when this construction can yield self-dual codes. We construct self-dual codes of various lengths over F2 and F2+uF2. Using extensions, neighbours and sequences of neighbours, we construct many new self-dual codes. In particular, we construct one new self-dual code of length 66 and 51 new self-dual codes of length 68.

AB - In this paper, we construct self-dual codes from a construction that involves both block circulant matrices and block quadratic residue circulant matrices. We provide conditions when this construction can yield self-dual codes. We construct self-dual codes of various lengths over F2 and F2+uF2. Using extensions, neighbours and sequences of neighbours, we construct many new self-dual codes. In particular, we construct one new self-dual code of length 66 and 51 new self-dual codes of length 68.

KW - Codes over rings

KW - Quadratic double circulant codes

KW - Self-dual codes

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New extremal binary self-dual codes from block circulant matrices and block quadratic residue circulant matrices

Abstract

Keywords

ASJC Scopus subject areas

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