Composite matrices from group rings, composite G-codes and constructions of self-dual codes

被引：6

作者：

Dougherty, Steven T. ^{[1
]}

Gildea, Joe ^{[2
]}

Korban, Adrian ^{[2
]}

Kaya, Abidin ^{[3
]}

机构：

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

[2] Univ Chester, Dept Math & Phys Sci, Thornton Sci Pk,Pool Ln, Chester CH2 4NU, Cheshire, England

[3] Harmony Sch Technol, Houston, TX 77038 USA

来源：

DESIGNS CODES AND CRYPTOGRAPHY | 2021年 / 89卷 / 07期

关键词：

Composite matrices; Group rings; Composite G-codes; Self-orthogonal composite G-codes; Codes over rings; Self-dual codes; II CODES; AUTOMORPHISM;

D O I：

10.1007/s10623-021-00882-8

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

In this work, we define composite matrices which are derived from group rings. We extend the idea of G-codes to composite G-codes. We show that these codes are ideals in a group ring, where the ring is a finite commutative Frobenius ring and G is an arbitrary finite group. We prove that the dual of a composite G-code is also a composite G-code. We also define quasi-composite G-codes. Additionally, we study generator matrices, which consist of the identity matrices and the composite matrices. Together with the generator matrices, the well known extension method, the neighbour method and its generalization, we find extremal binary self-dual codes of length 68 with new weight enumerators for the rare parameters gamma = 7, 8 and 9. In particular, we find 49 new such codes. Moreover, we show that the codes we find are inaccessible from other construction

引用

页码：1615 / 1638

页数：24