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The listdecoding size of reedmuller codes
 Electronic Colloquium on Computational Complexity (ECCC
"... In this work we study the listdecoding size of ReedMuller codes. Given a received word and a distance parameter, we are interested in bounding the size of the list of ReedMuller codewords that are within that distance from the received word. Previous bounds of Gopalan, Klivans and Zuckerman [4] o ..."
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In this work we study the listdecoding size of ReedMuller codes. Given a received word and a distance parameter, we are interested in bounding the size of the list of ReedMuller codewords that are within that distance from the received word. Previous bounds of Gopalan, Klivans and Zuckerman [4
ListDecoding ReedMuller codes over small fields
 IN PROC. 40 TH ACM SYMP. ON THEORY OF COMPUTING (STOC’08)
, 2008
"... We present the first local listdecoding algorithm for the r th order ReedMuller code RM(r, m) over F2 for r ≥ 2. Given an oracle for a received word R: F m 2 → F2, our randomized local listdecoding algorithm produces a list containing all degree r polynomials within relative distance (2 −r − ε) f ..."
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Cited by 22 (3 self)
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We present the first local listdecoding algorithm for the r th order ReedMuller code RM(r, m) over F2 for r ≥ 2. Given an oracle for a received word R: F m 2 → F2, our randomized local listdecoding algorithm produces a list containing all degree r polynomials within relative distance (2 −r − ε
Weight distribution and listdecoding size of ReedMuller codes
 in Proc. The First Symposium on Innovations in Computer Science (ICS 2010
"... Abstract: We study the weight distribution and listdecoding size of ReedMuller codes. Given a weight parameter, we are interested in bounding the number of ReedMuller codewords with a weight of up to the given parameter. Additionally, given a received word and a distance parameter, we are interes ..."
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Cited by 9 (1 self)
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Abstract: We study the weight distribution and listdecoding size of ReedMuller codes. Given a weight parameter, we are interested in bounding the number of ReedMuller codewords with a weight of up to the given parameter. Additionally, given a received word and a distance parameter, we
List decoding of ReedMuller codes
 in &quot;Proceedings of ACCT’9
, 2004
"... We construct list decoding algorithms for first order ReedMuller codes RM[1, m] of length n = 2m correcting up to n ( 1 2 − ɛ) errors with complexity O(nɛ−3). Considering probabilistic approximation of these algorithms leads to randomized list decoding algorithms with characteristics similar to Gol ..."
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Cited by 2 (0 self)
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We construct list decoding algorithms for first order ReedMuller codes RM[1, m] of length n = 2m correcting up to n ( 1 2 − ɛ) errors with complexity O(nɛ−3). Considering probabilistic approximation of these algorithms leads to randomized list decoding algorithms with characteristics similar
List Decoding of qary ReedMuller Codes 1)
, 2004
"... Abstract. The qary ReedMuller codes RMq(u, m) of length n = qm are a generalization of ReedSolomon 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 listdecoding algorithm ..."
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Abstract. The qary ReedMuller codes RMq(u, m) of length n = qm are a generalization of ReedSolomon 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 listdecoding
List decoding of second order ReedMuller codes
 In : Proceedings of the Eighteen International Symposium of Communication Theory and Applications, Ambleside
, 2005
"... A new list decoding algorithms for second order ReedMuller codes RM(2,m) of length n = 2m correcting far beyond minimal distance is proposed. In order to prove polynomial complexity of the algorithm we derive an improvement of well known Johnson bound. Key words: list decoding, complexity, ReedMul ..."
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Cited by 11 (0 self)
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A new list decoding algorithms for second order ReedMuller codes RM(2,m) of length n = 2m correcting far beyond minimal distance is proposed. In order to prove polynomial complexity of the algorithm we derive an improvement of well known Johnson bound. Key words: list decoding, complexity, ReedMuller
5 ListDecodable Codes
"... The field of coding theory is motivated by the problem of communicating reliably over noisy channels — where the data sent over the channel may come out corrupted on the other end, but we nevertheless want the receiver to be able to correct the errors and recover the original message. There is a vas ..."
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. ” In particular, a generalization of the notion of an errorcorrecting code yields a framework that we will use to unify all of the main pseudorandom objects covered in this survey (averaging samplers, expander graphs, randomness extractors, listdecodable codes, pseudorandom generators).
5 ListDecodable Codes
"... The field of coding theory is motivated by the problem of communicating reliably over noisy channels — where the data sent over the channel may come out corrupted on the other end, but we nevertheless want the receiver to be able to correct the errors and recover the original message. There is a vas ..."
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. ” In particular, a generalization of the notion of an errorcorrecting code yields a framework that we will use to unify all of the main pseudorandom objects covered in this survey (averaging samplers, expander graphs, randomness extractors, listdecodable codes, pseudorandom generators).
List Decoding ofary Reed–Muller Codes
"... Abstract—The qary Reed–Muller (RM) codes RM (u;m) of length n = q are a generalization of Reed–Solomon (RS) 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 listdecoding ..."
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Abstract—The qary Reed–Muller (RM) codes RM (u;m) of length n = q are a generalization of Reed–Solomon (RS) 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 listdecoding
Results 1  10
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100,582