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

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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.