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 50 条

[1] COMPOSITE CONSTRUCTIONS OF SELF-DUAL CODES FROM GROUP RINGS AND NEW EXTREMAL SELF-DUAL BINARY CODES OF LENGTH 68
Dougherty, Steven T.
Gildea, Joe
Korban, Adrian
Kaya, Abidin
ADVANCES IN MATHEMATICS OF COMMUNICATIONS, 2020, 14 (04) : 677 - 702
[2] Quadruple bordered constructions of self-dual codes from group rings
Steven T. Dougherty
Joseph Gildea
Abidin Kaya
Cryptography and Communications, 2020, 12 : 127 - 146
[3] Quadruple bordered constructions of self-dual codes from group rings
Dougherty, Steven T.
Gildea, Joseph
Kaya, Abidin
CRYPTOGRAPHY AND COMMUNICATIONS-DISCRETE-STRUCTURES BOOLEAN FUNCTIONS AND SEQUENCES, 2020, 12 (01): : 127 - 146
[4] Various constructions for self-dual codes over rings and new binary self-dual codes
Kaya, Abidin
Yildiz, Bahattin
DISCRETE MATHEMATICS, 2016, 339 (02) : 460 - 469
[5] An altered four circulant construction for self-dual codes from group rings and new extremal binary self-dual codes I
Gildea, Joe
Kaya, Abidin
Yildiz, Bahattin
DISCRETE MATHEMATICS, 2019, 342 (12)
[6] Group rings, G-codes and constructions of self-dual and formally self-dual codes
Dougherty, Steven T.
Gildea, Joseph
Taylor, Rhian
Tylyshchak, Alexander
DESIGNS CODES AND CRYPTOGRAPHY, 2018, 86 (09) : 2115 - 2138
[7] Group rings, G-codes and constructions of self-dual and formally self-dual codes
Steven T. Dougherty
Joseph Gildea
Rhian Taylor
Alexander Tylyshchak
Designs, Codes and Cryptography, 2018, 86 : 2115 - 2138
[8] Constructions of self-dual codes and formally self-dual codes over rings
Dougherty, Steven T.
Kaya, Abidin
Salturk, Esengul
APPLICABLE ALGEBRA IN ENGINEERING COMMUNICATION AND COMPUTING, 2016, 27 (05) : 435 - 449
[9] Constructions of self-dual codes and formally self-dual codes over rings
Steven T Dougherty
Abidin Kaya
Esengül Saltürk
Applicable Algebra in Engineering, Communication and Computing, 2016, 27 : 435 - 449
[10] 2n Bordered constructions of self-dual codes from group rings
Dougherty, Steven T.
Gildea, Joe
Kaya, Abidin
FINITE FIELDS AND THEIR APPLICATIONS, 2020, 67

← 1 2 3 4 5 →