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.
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页码：89 / 98
页数：10
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