Modified quadratic residue constructions and new extremal binary self-dual codes of lengths 64, 66 and 68

Joe Gildea; Holly Hamilton; Abidin Kaya; Bahattin Yildiz

doi:10.1016/j.ipl.2020.105927

Modified quadratic residue constructions and new extremal binary self-dual codes of lengths 64, 66 and 68

Joe Gildea, Holly Hamilton, Abidin Kaya, Bahattin Yildiz

Informatics, Computing, and Cyber Systems, School of

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

5 Scopus citations

Abstract

In this work we consider modified versions of quadratic double circulant and quadratic bordered double circulant constructions over the binary field and the rings F₂+uF₂ and F₄+uF₄ for different prime values of p. Using these constructions with extensions and neighbors we are able to construct a number of extremal binary self-dual codes of different lengths with new parameters in their weight enumerators. In particular we construct 2 new codes of length 64, 4 new codes of length 66 and 14 new codes of length 68. The binary generator matrices of the new codes are available online at [8].

Original language	English (US)
Article number	105927
Journal	Information Processing Letters
Volume	157
DOIs	https://doi.org/10.1016/j.ipl.2020.105927
State	Published - May 2020

Keywords

Codes over rings
Combinatorial problems
Extremal self-dual codes
Quadratic circulant matrices
Quadratic residues

ASJC Scopus subject areas

Theoretical Computer Science
Signal Processing
Information Systems
Computer Science Applications

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10.1016/j.ipl.2020.105927

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title = "Modified quadratic residue constructions and new extremal binary self-dual codes of lengths 64, 66 and 68",

abstract = "In this work we consider modified versions of quadratic double circulant and quadratic bordered double circulant constructions over the binary field and the rings F2+uF2 and F4+uF4 for different prime values of p. Using these constructions with extensions and neighbors we are able to construct a number of extremal binary self-dual codes of different lengths with new parameters in their weight enumerators. In particular we construct 2 new codes of length 64, 4 new codes of length 66 and 14 new codes of length 68. The binary generator matrices of the new codes are available online at [8].",

keywords = "Codes over rings, Combinatorial problems, Extremal self-dual codes, Quadratic circulant matrices, Quadratic residues",

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

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T1 - Modified quadratic residue constructions and new extremal binary self-dual codes of lengths 64, 66 and 68

AU - Gildea, Joe

AU - Hamilton, Holly

AU - Kaya, Abidin

AU - Yildiz, Bahattin

PY - 2020/5

Y1 - 2020/5

N2 - In this work we consider modified versions of quadratic double circulant and quadratic bordered double circulant constructions over the binary field and the rings F2+uF2 and F4+uF4 for different prime values of p. Using these constructions with extensions and neighbors we are able to construct a number of extremal binary self-dual codes of different lengths with new parameters in their weight enumerators. In particular we construct 2 new codes of length 64, 4 new codes of length 66 and 14 new codes of length 68. The binary generator matrices of the new codes are available online at [8].

AB - In this work we consider modified versions of quadratic double circulant and quadratic bordered double circulant constructions over the binary field and the rings F2+uF2 and F4+uF4 for different prime values of p. Using these constructions with extensions and neighbors we are able to construct a number of extremal binary self-dual codes of different lengths with new parameters in their weight enumerators. In particular we construct 2 new codes of length 64, 4 new codes of length 66 and 14 new codes of length 68. The binary generator matrices of the new codes are available online at [8].

KW - Codes over rings

KW - Combinatorial problems

KW - Extremal self-dual codes

KW - Quadratic circulant matrices

KW - Quadratic residues

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Modified quadratic residue constructions and new extremal binary self-dual codes of lengths 64, 66 and 68

Abstract

Keywords

ASJC Scopus subject areas

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