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It has been proved that the maximum likelihood decoding problem of Reed-Solomon codes is NP-hard. However, the length of the code in the proof is at most polylogarithmic in the size of the alphabet. For the complexity of maximum likelihood decoding of the primitive Reed-Solomon code, whose length is one less than the size of alphabet, the only known result states that it is at least as hard as the...
The characterization of the access structures of ideal secret sharing schemes is one of the main open problems in secret sharing and has important connections with matroid theory. In the EUROCRYPT'07, Farras made a important contribution to this work by using discrete polymatroids. In particular, they further gave a very difficult open problem, that is, characterizing the representable discrete polymatroids,...
Memory bounded functions have been designed to combat email spams in a sequence of papers. The cost of computing the functions is usually dominated by random walks over large tables that cannot be put in CPU cache. In this paper, we propose a simple number theoretic way of generating such tables based on exponentiations of sparse polynomials modulo sparse irreducible polynomials over finite fields...
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