A Generalized Construction and Improvements on Nonbinary Codes From Goppa Codes

被引：4

作者：

Tomlinson, Martin ^{[1
]}

Jibril, Mubarak ^{[1
]}

Tjhai, Cen ^{[1
]}

Bezzateev, Sergey V. ^{[3
]}

Grassl, Markus ^{[2
]}

Ahmed, Mohammed Zaki ^{[1
]}

机构：

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

[2] Natl Univ Singapore, Ctr Quantum Technol, Singapore 117543, Singapore

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

来源：

IEEE TRANSACTIONS ON INFORMATION THEORY | 2013年 / 59卷 / 11期

关键词：

Goppa; BCH; Reed-Solomon; error correction; BINARY-CODES;

D O I：

10.1109/TIT.2013.2276626

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

We present an efficient construction of extended length Goppa codes. Using this construction, we obtain 78 new nonbinary codes with better minimum distance than the previously known codes with the same length and dimension. The construction is based on the observation that certain Goppa codes can be seen as BCH codes.

引用

页码：7299 / 7304

页数：6

共 50 条

[1] A Generalized Construction of Extended Goppa Codes
Jibril, Mubarak
Bezzateev, Sergey V.
Tomlinson, Martin
Grassl, Markus
Ahmed, Mohammed Zaki
IEEE TRANSACTIONS ON INFORMATION THEORY, 2014, 60 (09) : 5296 - 5303
[2] Using the Structure of Subfields in the Construction of Goppa Codes and Extended Goppa Codes
Tomlinson, Martin
Bezzateev, Sergey V.
Jibril, Mubarak
Ambroze, Marcel A.
Ahmed, Mohammed Zaki
IEEE TRANSACTIONS ON INFORMATION THEORY, 2015, 61 (06) : 3214 - 3224
[3] Generalized geometric Goppa codes
Heydtmann, AE
COMMUNICATIONS IN ALGEBRA, 2002, 30 (06) : 2763 - 2789
[4] Nonbinary quantum codes derived from generalized Hermitian codes
Qian, J. (qianjianfa@yahoo.com.cn), 1600, Binary Information Press, P.O. Box 162, Bethel, CT 06801-0162, United States (09):
[5] A METHOD FOR DECODING OF GENERALIZED GOPPA CODES
MANDELBAUM, DM
IEEE TRANSACTIONS ON INFORMATION THEORY, 1978, 24 (02) : 268 - 268
[6] Decoding of (Interleaved) Generalized Goppa Codes
Liu, Hedongliang
Pircher, Sabine
Zeh, Alexander
Wachter-Zeh, Antonia
2021 IEEE INTERNATIONAL SYMPOSIUM ON INFORMATION THEORY (ISIT), 2021, : 664 - 669
[7] METHOD FOR DECODING OF GENERALIZED GOPPA CODES
MANDELBAUM, DM
IEEE TRANSACTIONS ON INFORMATION THEORY, 1977, 23 (01) : 137 - 140
[8] CLASSIFICATION OF GENERALIZED BCH CODES AND SOME PROPERTIES OF GOPPA CODES
SUGIYAMA, Y
HIRASAWA, S
KASAHARA, M
NAMEKAWA, T
ELECTRONICS & COMMUNICATIONS IN JAPAN, 1975, 58 (12): : 9 - 16
[9] Construction of binary linear codes through geometric Goppa codes
Construção de códigos lineares binários através de códigos geométricos de Goppa
Da Câmara, M.A. (camara@ufu.br), 2005, University Federal de Uberlandia, P.O. Box 593, Uberlandia, 38400-902, Brazil (14):
[10] Codes Derived from Binary Goppa Codes
P. Loidreau
Problems of Information Transmission, 2001, 37 (2) : 91 - 99

← 1 2 3 4 5 →