On the Minimum Distance of Concatenated Codes and Decoding Method up to the True Minimum Distance

Toshiyuki KOHNOSU  Toshihisa NISHIJIMA  Shigeichi HIRASAWA  

Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E80-A   No.11   pp.2111-2116
Publication Date: 1997/11/25
Online ISSN: 
DOI: 
Print ISSN: 0916-8508
Type of Manuscript: Special Section PAPER (Special Section on Information Theory and Its Applications)
Category: Coding Theory
Keyword: 
concatenated code,  minimum distance,  complete weight enumerator,  Reddy-Robinson algorithm,  decoding method beyond the BCH bound,  

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Summary: 
Concatenated codes have many remarkable properties from both the theoretical and practical viewpoints. The minimum distance of a concatenated code is at least the product of the minimum distances of an outer code and an inner code. In this paper, we shall examine some cases that the minimum distance of concatenated codes is beyond the lower bound and get the tighter bound or the true minimum distance of concatenated codes by using the complete weight enumerator of the outer code and the Hamming weight enumerator of the inner code. Furthermore we propose a new decoding method based on Reddy-Robinson algorithm by using the decoding method beyond the BCH bound.