| 设计距离为7的q元BCH码的周期分布 |
| |
| 引用本文： | 陈小松,王春鹏.设计距离为7的q元BCH码的周期分布[J].湖南大学学报(自然科学版),2007,34(11):84-87. |
| |
| 作者姓名： | 陈小松 王春鹏 |
| |
| 作者单位： | 中南大学,数学科学与计算技术学院,湖南,长沙,410083 |
| |
| 基金项目： | 国家自然科学基金资助项目(10771058)，湖南省自然科学基金资助项目(05JJ30141) |
| |
| 摘 要： | 通过对循环陪集的研究及利用分圆多项式的一个性质,得到了设计距离为7的q元BCH码的周期分布计算公式:码的周期分布为q的幂,当码的周期不等于某些特殊值时,幂为码长与周期的最大公因数.当码的周期为特殊值时,幂为n/b-m6/b],这里n是码的长度,b是由n和码的周期决定的2到6之间的整数,m是q模n的指数.由此计算公式和Mobius反转公式给出了无内周期码字个数的计数结果.
|
| 关 键 词： | 循环码 BCH码 循环陪集 周期分布 |
| 文章编号： | 1000-2472（2007）11-0084-04 |
| 修稿时间： | 2007-04-27 |
Period Distributions of q-ary BCH Codes with Designed Distance 7 |
| |
| CHEN Xiao-song,WANG Chun-peng.Period Distributions of q-ary BCH Codes with Designed Distance 7[J].Journal of Hunan University(Naturnal Science),2007,34(11):84-87. |
| |
| Authors: | CHEN Xiao-song WANG Chun-peng |
| |
| Institution: | College of Mathematical Sciences and Computational Technology, Central South Univ, Changsha,Hunan 410083 ,China |
| |
| Abstract: | The calculation formulae for period distribution of q-ary BCH codes with designed distance 7 were obtained based on the discussion of cyclotomic cosets and property of cyclotomic polynomials: the period distribution is q's power.When the period was unequal to some special values,the power was the GCD of code-length and the period.When the period was of special value,the power was n/b-m;where n was the code-length,b was some number among 2 to 6 related to n and the period,and m was the index of q module n.The nonperiodic cyclic equivalence classes of this kind of codes could be counted due to the period distribution formula and the Mobuis inverse formula |
| |
| Keywords: | cyclic codes BCH codes cyclotomic cosets period distribution |
| 本文献已被 CNKI 维普 万方数据 等数据库收录！ |
| 点击此处可从《湖南大学学报(自然科学版)》浏览原始摘要信息 |
| 点击此处可从《湖南大学学报(自然科学版)》下载免费的PDF全文 |
