List Decoding of<tex>$q$</tex>-ary Reed–Muller Codes
نویسندگان
چکیده
منابع مشابه
List Decoding of q - ary Reed - Muller Codes 1 )
The q-ary Reed-Muller codes RMq(u,m) of length n = q are a generalization of Reed-Solomon codes, which use polynomials in m variables to encode messages through functional encoding. Using an idea of reducing the multivariate case to the univariate case, randomized list-decoding algorithms for Reed-Muller codes were given in [1] and [15]. The algorithm in [15] is an improvement of the algorithm ...
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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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Abstract. A binary code is said to be a disjunctive list-decoding sL-code, s ≥ 1, L ≥ 1, (briefly, LD sL-code) if the code is identified by the incidence matrix of a family of finite sets in which the union of any s sets can cover not more than L− 1 other sets of the family. In this paper, we introduce a natural probabilistic generalization of LD sL-code when the code is said to be an almost di...
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ژورنال
عنوان ژورنال: IEEE Transactions on Information Theory
سال: 2004
ISSN: 0018-9448
DOI: 10.1109/tit.2004.825043