一类新的能够渐进达到Gilbert-Varshamov界的Alternant子类码

樊继豪, 陈汉武

电子学报 ›› 2015, Vol. 43 ›› Issue (11) : 2243-2246.

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电子学报 ›› 2015, Vol. 43 ›› Issue (11) : 2243-2246. DOI: 10.3969/j.issn.0372-2112.2015.11.016
学术论文

一类新的能够渐进达到Gilbert-Varshamov界的Alternant子类码

  • 樊继豪1, 陈汉武1,2
作者信息 +

A New Subclass of Alternant Codes Can Meet the Gilbert-Varshamov Bound

  • FAN Ji-hao1, CHEN Han-wu1,2
Author information +
文章历史 +

摘要

本文基于Maximum Distance Separable(MDS)码的Hamming重量分布提出一类新的二元Alternant子类码.分析表明这类新的子类码包含整个BCH码类,并且可以渐进达到Gilbert-Varshamov(GV)界.

Abstract

A new subclass of binary Alternant codes is proposed based on the Hamming weight distribution of Maximum Distance Separable(MDS) codes.It is shown that the new codes include the whole BCH codes subclass and can asymptotically meet the Gilbert-Varshamov(GV) bound.

关键词

Alternant码 / BCH码 / Gilbert-Varshamov界 / Hamming重量分布 / Maximum Distance Separable(MDS)码

Key words

Alternant codes / BCH codes / Gilbert-varshamov bound / Hamming weight distribution / Maximum distance separable(MDS) codes

引用本文

导出引用
樊继豪, 陈汉武. 一类新的能够渐进达到Gilbert-Varshamov界的Alternant子类码[J]. 电子学报, 2015, 43(11): 2243-2246. https://doi.org/10.3969/j.issn.0372-2112.2015.11.016
FAN Ji-hao, CHEN Han-wu. A New Subclass of Alternant Codes Can Meet the Gilbert-Varshamov Bound[J]. Acta Electronica Sinica, 2015, 43(11): 2243-2246. https://doi.org/10.3969/j.issn.0372-2112.2015.11.016
中图分类号: TN911.22   

参考文献

[1] MacWilliams F J,Sloane N J A.The Theory of Error-Correcting Codes[M]. Amsterdam:The Netherlands:North-Holland,1981.1-369.
[2] 冯克勤.纠错码的代数理论[M]. 北京:清华大学出版社,2005.1-80. Keqin Feng.The Algebraic Theory of Error-Correcting Codes[M]. Beijing:Tsinghua University Press,2005.1-80.(in Chinese)
[3] Berlekamp E.Goppa codes[J]. IEEE Transactions on Information Theory,1973,19(5):590-592.
[4] Martinez-Perez C,Willems W.Is the class of cyclic codes asymptotically good?[J]. IEEE Transactions on Information Theory,2006,52(2):696-700.
[5] Ezerman M F,Grassl M,Sole P.The weights in MDS codes[J]. IEEE Transactions on Information Theory,2011,57(1):392-396.

基金

国家自然科学基金 (No.61170321); 高等学校博士学科点专项科研基金 (No.20110092110024); 江苏省普通高校研究生科研创新计划 (No.CXZZ13_0105)

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