On Reed-Solomon Codes

被引：1
|
作者：
Qunying LIAO1 1Institution of Mathematics and Software Science
机构：
来源：
Chinese Annals of Mathematics(Series B) | 2011年 / 32卷 / 01期
基金：
中国国家自然科学基金;
关键词：
Reed-Solomon code; Weil bound; Error distance; Rational function; Trace Reed-Solomon code; Trace map;
D O I：
暂无
中图分类号：
O157.4 [编码理论（代数码理论）];
学科分类号：
070104 ;
摘要：
The complexity of decoding the standard Reed-Solomon code is a well-known open problem in coding theory.The main problem is to compute the error distance of a received word.Using the Weil bound for character sum estimate,Li and Wan showed that the error distance can be determined when the degree of the received word as a polynomial is small.In the first part,the result of Li and Wan is improved.On the other hand,one of the important parameters of an error-correcting code is the dimension.In most cases,one can only get bounds for the dimension.In the second part,a formula for the dimension of the generalized trace Reed-Solomon codes in some cases is obtained.
引用
下载
收藏
页码：89 / 98
页数：10
相关论文
共 50 条
  • [31] Quantum Generalized Reed-Solomon codes
    State Key Laboratory of Integrated Service Networks, Xidian University, Xi'an 710071, China
    Wuli Xuebao, 2008, 1 (28-30):
  • [32] Duals of linearized Reed-Solomon codes
    Caruso, Xavier
    Durand, Amaury
    DESIGNS CODES AND CRYPTOGRAPHY, 2023, 91 (01) : 241 - 271
  • [33] Systematic modified Reed-Solomon codes
    Weng, LJ
    Shen, BZ
    Mo, SH
    GLOBECOM 97 - IEEE GLOBAL TELECOMMUNICATIONS CONFERENCE, CONFERENCE RECORD, VOLS 1-3, 1997, : 1245 - 1249
  • [34] Multidimensional extension of Reed-Solomon codes
    Shen, BZ
    Tzeng, KK
    1998 IEEE INTERNATIONAL SYMPOSIUM ON INFORMATION THEORY - PROCEEDINGS, 1998, : 54 - 54
  • [35] Subspace subcodes of Reed-Solomon codes
    Hattori, M
    McEliece, RJ
    Solomon, G
    IEEE TRANSACTIONS ON INFORMATION THEORY, 1998, 44 (05) : 1861 - 1880
  • [36] On Expanded Cyclic and Reed-Solomon Codes
    Wu, Yingquan
    IEEE TRANSACTIONS ON INFORMATION THEORY, 2011, 57 (02) : 601 - 620
  • [37] Reed-Solomon Codes for Satellite Communications
    Liu, Yongmei
    Guan, Yong
    Zhang, Jie
    Wang, Guohui
    Zhang, Yan
    2009 IITA INTERNATIONAL CONFERENCE ON CONTROL, AUTOMATION AND SYSTEMS ENGINEERING, PROCEEDINGS, 2009, : 246 - +
  • [38] On error distance of Reed-Solomon codes
    Li YuJuan
    Wan DaQing
    SCIENCE IN CHINA SERIES A-MATHEMATICS, 2008, 51 (11): : 1982 - 1988
  • [39] Sequential Decoding of Reed-Solomon Codes
    Miloslavskaya, Vera
    Trifonov, Peter
    2014 INTERNATIONAL SYMPOSIUM ON INFORMATION THEORY AND ITS APPLICATIONS (ISITA), 2014, : 453 - 457
  • [40] Weighted Reed-Solomon convolutional codes
    Alfarano, Gianira N. N.
    Napp, Diego
    Neri, Alessandro
    Requena, Veronica
    LINEAR & MULTILINEAR ALGEBRA, 2024, 72 (05): : 841 - 874
12345