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Journals and Conferences
The decoding capabilities of algebraic algorithms, mainly the Berlekamp-Massey algorithm, the Euclidean algorithm and our generalizations of these algorithms, are basically constrained by the minimum distance bounds of the codes. Thus, when the actual minimum distance of the codes is greater than that given by the bounds, these algorithms usually cannot… (More)
Newton's identities have played a significant role in decoding and minimum distance determination of cyclic and BCH codes. This paper carries the notion over from cyclic codes to algebraic-geometric (AG) codes and introduces Newton's identities for AG codes, also for the purpose of minimum distance determination and decoding.
In this paper, a new procedure for decoding cyclic and BCH codes up to their actual minimum distance is presented. Previous algebraic decoding procedures for cyclic and BCH codes such as the Peterson decoding procedure and our procedure using nonrecurrent syndrome dependence relations can be regarded as special cases of this new decoding procedure. With the… (More)