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Algebraic decoding beyond eBCH of some binary cyclic codes, when e>eBCH

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4 Author(s)
Bours, P. ; Dept. of Math. & Comput. Sci., Eindhoven Univ. of Technol., Netherlands ; Janssen, J.C.M. ; Van Asperdt, M. ; Van Tilborg, H.C.A.

For a number of binary cyclic codes with e>e BCH, algebraic algorithms are given to find the error locator polynomial. Thus, for these codes more errors can be corrected algebraically than by the Berlekamp-Massey algorithm. In some cases, all error patterns of weight up to e can be decoded; in other cases, only error patterns of weight up to e' with e BCH<e'⩽e can be decoded. The correctness of three of these algorithms is (partly) based on an exhaustive computer search; in all other cases, the algebraic proof is given in detail. It seems likely that many more cyclic codes can be decoded with these methods

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Information Theory, IEEE Transactions on  (Volume:36 ,  Issue: 1 )