Some decoding applications of minimal realization
We show that minimal realization (MR) of a finite sequence and the associated MR algorithm  provide new solutions to a number of decoding problems: BCH and Reed-Solomon codes, errors and erasures, classical Goppa codes and negacyclic codes. We concentrate on the MR of the DFT of an error polynomial, thus avoiding the “key equation” and Forney's procedure. We also discuss simplification of the theory in characteristic two and an extension of the MR theory to several sequences, obtaining a new simultaneous MR algorithm.
KeywordsCyclic Code Minimal Polynomial Weight Enumerator Minimal Realization Goppa Code
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