Using the Structure of Subfields in the Construction of Goppa Codes and Extended Goppa Codes

被引：5

作者：

Tomlinson, Martin ^{[1
]}

Bezzateev, Sergey V. ^{[2
]}

Jibril, Mubarak ^{[3
]}

Ambroze, Marcel A. ^{[1
]}

Ahmed, Mohammed Zaki ^{[1
]}

机构：

[1] Univ Plymouth, Sch Comp & Math, Plymouth PL4 8AA, Devon, England

[2] St Petersburg State Univ Aerosp Instrumentat, Dept Technol Informat Secur, St Petersburg 190000, Russia

[3] Nigerian Commun Satellite Ltd, Abuja 932001, Nigeria

来源：

IEEE TRANSACTIONS ON INFORMATION THEORY | 2015年 / 61卷 / 06期

关键词：

Codes; Goppa; BCH; Reed Solomon; error correction coding;

D O I：

10.1109/TIT.2015.2419613

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

It is shown that for some location sets and some integral multiple power Galois fields that some new general subclasses of Goppa codes may be defined which have improved lower bounds to code dimension and minimum distance compared with ordinary Goppa codes. Some previously published results are shown to be particular cases of these general subclasses of codes. A new subclass of reversible Goppa codes is also presented. Examples of code construction for these subclasses, demonstrating the improved code parameters, are presented for both non binary and binary codes.

引用

页码：3214 / 3224

页数：11

共 21 条

[1] Linear and nonlinear constructions of DNA codes with Hamming distance d, constant GC-content and a reverse-complement constraint [J].

Aboluion, Niema ;

Smith, Derek H. ;

Perkins, Stephanie .

DISCRETE MATHEMATICS, 2012, 312 (05) :1062-1075

[2]

[Anonymous], 1978, The Theory of Error-Correcting Codes

[3]

[Anonymous], 1970, PROBLEMY PEREDACHI I

[4]

[Anonymous], 2007, BOUNDS MINIMUM DISTA

[5] On the cyclicity of goppa codes, parity-check subcodes of Goppa codes, and extended Goppa codes [J].

Berger, TP .

FINITE FIELDS AND THEIR APPLICATIONS, 2000, 6 (03) :255-281

[6] Quasi-cyclic Goppa codes. [J].

Berger, TP .

2000 IEEE INTERNATIONAL SYMPOSIUM ON INFORMATION THEORY, PROCEEDINGS, 2000, :195-195

[7] Goppa and related codes invariant under a prescribed permutation [J].

Berger, TP .

IEEE TRANSACTIONS ON INFORMATION THEORY, 2000, 46 (07) :2628-2633

[8] Subclass of Cyclic Goppa Codes [J].

Bezzateev, Sergey V. ;

Shekhunova, Natalia A. .

IEEE TRANSACTIONS ON INFORMATION THEORY, 2013, 59 (11) :7379-7385

[9] New identities relating wild Goppa codes [J].

Couvreur, Alain ;

Otmani, Ayoub ;

Tillich, Jean-Pierre .

FINITE FIELDS AND THEIR APPLICATIONS, 2014, 29 :178-197

[10]

Das P. K., 2012, INT J ALGEBRA, V6, P185

← 1 2 3 →