Coding and fast decoding for linear codes with soft and bit-level decision

1. 从实践和理论的角度看，一类线性码是非常重要的。为了讨论误差性能分析，我们需要最小距离。然而，当线性码有很多码字时，计算最小距离是很困难的。提出了一种计算线性码最小距离的有效算法。该方法以搜索树为基础，利用线性码的奇偶校验矩阵的性质。构建比任何已知的相同长度和最小距离的代码包含更多码字的最佳代码的研究正在稳步进行。提出了一种构造良好线性码的方法。它是基于奇偶校验矩阵的一些性质和计算机搜索的帮助。缩短里德-所罗门码（RS）是一类重要的纠错码。然而，迄今为止，这类研究的报告显然尚未发表。讨论了缩短的RS码及其译码算法，并对其译码算法进行了扩展，使其能够纠错比BCH所指示的错误更多。

1. A class of linear code is very important as practical and theoretical points of view. For discussing the error performance analysis, we need the minimum distance. However it is hard to compute the minimum distance when the linear code has a great many codewords. An efficient algorithm of computing the minimum distance of linear code is presented. The method is based upon the searching tree and using the property of parity check matrix for linear code.2. A study of constructing the best code, contain more codewords than any previously known codes of same length and minimum distance, is being continued steadily. A method for constructing good linear code is presented. It is based upon in some properties of parity check matrices and help of a computer search.3. Shortened Reed-Solomon (RS) codes are practically important class of error correcting codes. However reports of this type of research have apparently not been published to date. The shortened RS code and its decoding algorithm which is extended to correct more errors than indicated by the BCH are discussed.bounds.