摘要
循环码的极小距离大于或等于其BCH界 .本文考虑的是极小距离等于BCH界的特殊情形 .利用一类自反循环码的事实 ,证明了使循环码的极小距离等于其BCH界的两个充分条件 ;并指出极小距离等于任意给定值、维数任意大的循环码可以构造 .
It is well known that the minimum distance of a cyclic code is lower bounded by the BCH bound. This paper is concerned with the special case in which the minimum distance equals the BCH bound. By means of the fact of certain reversible cyclic codes, two sufficient conditions for the minimum distance of a cyclic code to equal its BCH bound have been found. And such a code of large enough dimension and any given minimum distance can be constructed.
出处
《数学杂志》
CSCD
北大核心
2002年第2期165-168,共4页
Journal of Mathematics
基金
国家自然科学基金资助项目
关键词
循环码
极小距离
BCH界
自反多项式
自反循环码
cyclic codes
minimum distance
BCH bound
self-reciprocal polynomial
reversible cyclic codes
