[1]孙露燕,张胜元*.一类码长是pm的2元BCH码的维数和重量分布[J].泉州师范学院学报,2019,(06):34-38.
 SUN Luyan,ZHANG Shengyuan*.The Dimension and Weight Distribution of a Class of Binary BCH Codes with Length pm[J].,2019,(06):34-38.
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一类码长是pm的2元BCH码的维数和重量分布()
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《泉州师范学院学报》[ISSN:1006-6977/CN:61-1281/TN]

卷:
期数:
2019年06期
页码:
34-38
栏目:
数学·计算科学
出版日期:
2019-12-15

文章信息/Info

Title:
The Dimension and Weight Distribution of a Class of Binary BCH Codes with Length pm
文章编号:
1009-8224(2019)06-0034-05
作者:
孙露燕张胜元*
福建师范大学 数学与信息学院,福建 福州 350117
Author(s):
SUN Luyan ZHANG Shengyuan*
School of Mathematics and Information Science, Fujian Normal University,Fujian 350117,China
关键词:
循环码 BCH码 维数 重量分布
Keywords:
cyclic codes BCH codes dimension weight distribution
分类号:
O157.4
文献标志码:
A
摘要:
循环码因其高效的编码译码算法而被广泛应用于通信系统、存储设备和消费类电子产品中,可见循环码是有广泛应用的线性码.BCH 码是一类特殊的循环码,因其良好的纠错能力通常被认为是最好的循环码之一,然而确定BCH码的维数和重量分布仍然是个开放的问题.文章主要研究2 元BCH码的维数和重量分布,并在码长是pm且2是模pm的原根的条件下,确定了其维数和重量分布,其中参数为[pm,2,2·pm-1]的2元BCH码是Plotkin界意义下的最优循环码.
Abstract:
Cyclic codes are widely used in data storage devices,communication systems,and consumer electronics due to their effective encoding and decoding algorithms.This fact demonstrates the importance of cyclic codes.In theory,BCH codes are among the best cyclic codes in terms of their error-correcting capability, but determining the dimension and weight distribution of BCH codes are still an open problem.This paper focus on binary BCH codes, the dimensions and distributions of binary BCH codes with length pm are determined, under the condition that 2 is a primitive root.As a consequence,optimal cyclic codes with parameters[pm,2,2·pm-1]with respect to the Plotkin's bound is presented.

参考文献/References:

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备注/Memo

备注/Memo:
收稿日期:2019-08-01
通信作者:张胜元(1966-),男,福建连城人,教授,博士,从事组合数学、编码理论、密码学研究,E-mail:syzhang@fjnu.edu.cn.
基金项目:国家自然科学基金(61572132); 福建省自然科学基金(2019J01275)
更新日期/Last Update: 2019-12-15