A Root-Finding Algorithm for List Decoding of Reed–Muller Codes
نویسندگان
چکیده
منابع مشابه
Efficient root-finding algorithm with application to list decoding of Algebraic-Geometric codes
A list decoding for an error-correcting code is a decoding algorithm that generates a list of codewords within a Hamming distance from the received vector, where can be greater than the error-correction bound. In [18], a list-decoding procedure for Reed–Solomon codes [19] was generalized to algebraic–geometric codes. A recent work [8] gives improved list decodings for Reed–Solomon codes and alg...
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The interpolation step of Sudan’s list decoding of Reed-Solomon codes sets forth the problem of finding the minimal polynomial of the ideal of interpolating polynomials with respect to a certain monomial order. An efficient algorithm that solves the problem is presented based on the theory of Gröbner bases of modules. In a special case, this algorithm is shown to be equivalent with the Berlekam...
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We briefly survey some recent progress on list decoding algorithms for binary codes. The results discussed include: – Algorithms to list decode binary Reed-Muller codes of any order up to the minimum distance, generalizing the classical GoldreichLevin algorithm for RM codes of order 1 (Hadamard codes). These algorithms are “local” and run in time polynomial in the message length. – Construction...
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ژورنال
عنوان ژورنال: IEEE Transactions on Information Theory
سال: 2005
ISSN: 0018-9448
DOI: 10.1109/tit.2004.842765