Bordered constructions of self-dual codes from group rings and new extremal binary self-dual codes

被引：21

作者：

Dougherty, Steven T. ^{[1
]}

Gildea, Joseph ^{[2
]}

Korban, Adrian ^{[2
]}

Kaya, Abidin ^{[3
]}

Tylyshchak, Alexander ^{[4
]}

Yildiz, Bahattin ^{[5
]}

机构：

[1] Univ Scranton, Dept Math, Scranton, PA 18510 USA

[2] Univ Chester, Dept Math, Chester, Cheshire, England

[3] Sampoerna Acad, LAve Campus, Jakarta 12780, Indonesia

[4] Uzhgorod State Univ, Dept Algebra, Uzhgorod, Ukraine

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

来源：

FINITE FIELDS AND THEIR APPLICATIONS | 2019年 / 57卷

关键词：

Group rings; Self-dual codes; Codes over rings; Extremal codes; Bordered constructions; DOUBLE-CIRCULANT; AUTOMORPHISM;

D O I：

10.1016/j.ffa.2019.02.004

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We introduce a bordered construction over group rings for self-dual codes. We apply the constructions over the binary field and the ring F-2 + uF(2), using groups of orders 9, 15, 21, 25, 27, 33 and 35 to find extremal binary self-dual codes of lengths 20, 32, 40, 44, 52, 56, 64, 68, 88 and best known binary self-dual codes of length 72. In particular we obtain 41 new binary extremal self-dual codes of length 68 from groups of orders 15 and 33 using neighboring and extensions. All the numerical results are tabulated throughout the paper. (C) 2019 Elsevier Inc. All rights reserved.

引用

页码：108 / 127

页数：20

共 23 条

[1] THE EXTENDED GOLAY CODES CONSIDERED AS IDEALS [J].