Generalized minimum distance decoding
IEEE Transactions on Information Theory
Shift-register synthesis and BCH decoding
IEEE Transactions on Information Theory
An erasures-and-errors decoding algorithm for Goppa codes (Corresp.)
IEEE Transactions on Information Theory
Decoding of alternant codes (Corresp.)
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
A new Reed-Solomon code decoding algorithm based on Newton's interpolation
IEEE Transactions on Information Theory
An efficient soft-decision Reed-Solomon decoding algorithm
IEEE Transactions on Information Theory
A Unifying System-Theoretic Framework for Errors-and-Erasures Reed-Solomon Decoding
AAECC-14 Proceedings of the 14th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
The probabilistic theory of the joint linear complexity of multisequences
SETA'06 Proceedings of the 4th international conference on Sequences and Their Applications
Efficient Linear Feedback Shift Registers with Maximal Period
Finite Fields and Their Applications
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In this paper, it is shown that the problem of generalized-minimum-distance (GMD) decoding of Reed-Solomon (RS) codes can be reduced to the problem of multisequence shift register synthesis, and a simple algorithm is presented that yields a solution for this problem by finding, for k = 1, 2, . . . , the shortest linear feedback shift register that can generate each of the first k sequences of a special kind of multisequence. The algorithm is based on the well-known Berlekamp-Massey algorithm for a single-sequence problem and is only a little more complex than it. Also presented is a GMD decoding algorithm for RS codes which employs the proposed multisequence shift register synthesis algorithm and whose complexity is less than 3nd + 8d^2 for the code length n and the minimum distance d. This GMD decoding algorithm provides an alternative to algorithms based on the Welch-Berlekamp algorithm.