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

被引：5

作者：

Gildea, Joe ^{[1
]}

Hamilton, Holly ^{[1
]}

Kaya, Abidin ^{[2
]}

Yildiz, Bahattin ^{[3
]}

机构：

[1] Univ Chester, Fac Sci & Engn, Dept Math, Chester, Cheshire, England

[2] Sampoerna Univ, Dept Math Educ, Jakarta 12780, Indonesia

[3] No Arizona Univ, Dept Math & Stat, Flagstaff, AZ 86001 USA

来源：

INFORMATION PROCESSING LETTERS | 2020年 / 157卷

关键词：

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

D O I：

10.1016/j.ipl.2020.105927

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

In this work we consider modified versions of quadratic double circulant and quadratic bordered double circulant constructions over the binary field and the rings F-2 + uF(2) and F-4 + uF(4) 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]. (C) 2020 Elsevier B.V. All rights reserved.

引用

页数：8

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