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On the stopping redundancy of ReedMuller codes
 IEEE TRANS. INFORM. THEORY
, 2006
"... The stopping redundancy of the code is an important parameter which arises from analyzing the performance of a linear code under iterative decoding on a binary erasure channel. In this paper, we will consider the stopping redundancy of Reed–Muller codes and related codes. Let ( ) be the Reed–Muller ..."
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Cited by 14 (0 self)
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The stopping redundancy of the code is an important parameter which arises from analyzing the performance of a linear code under iterative decoding on a binary erasure channel. In this paper, we will consider the stopping redundancy of Reed–Muller codes and related codes. Let ( ) be the Reed–Muller
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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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
Notes on ReedMuller codes
, 901
"... In this paper, we consider the ReedMuller (RM) codes. For the first order RM code, we prove that it is unique in the sense that any linear code with the same length, dimension and minimum distance must be the first order RM code; For the second order RM code, we give a constructive linear subcode ..."
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In this paper, we consider the ReedMuller (RM) codes. For the first order RM code, we prove that it is unique in the sense that any linear code with the same length, dimension and minimum distance must be the first order RM code; For the second order RM code, we give a constructive linear subcode
ReedMuller Codes
"... function obtained by taking w to be the Fourier spectrum is optimal in some sense. (Perhaps the reader will sense a challenge in this.) Finally, we remark that the above threshold decoding technique is generally applicable to all linear codes over GF(p) (whether block, cyclic, convolutional, or what ..."
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function obtained by taking w to be the Fourier spectrum is optimal in some sense. (Perhaps the reader will sense a challenge in this.) Finally, we remark that the above threshold decoding technique is generally applicable to all linear codes over GF(p) (whether block, cyclic, convolutional
Extractors from ReedMuller Codes
 In Proceedings of the 42nd Annual IEEE Symposium on Foundations of Computer Science
, 2001
"... Finding explicit extractors is an important derandomization goal that has received a lot of attention in the past decade. This research has focused on two approaches, one related to hashing and the other to pseudorandom generators. A third view, regarding extractors as good error correcting codes, w ..."
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Cited by 39 (4 self)
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, was noticed before. Yet, researchers had failed to build extractors directly from a good code, without using other tools from pseudorandomness. We succeed in constructing an extractor directly from a ReedMuller code. To do this, we develop a novel proof technique. Furthermore, our construction is the first
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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Cited by 1 (0 self)
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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
List Decoding of qary ReedMuller Codes
 IEEE Trans. Inform. Theory
, 2004
"... The qary ReedMuller codes RMq(u, m) of length n = qm are a generalization of ReedSolomon codes, which allow polynomials in m variables to encode the message. Using an idea of reducing the multivariate case to univariate case, randomized listdecoding algorithms for ReedMuller codes were given in ..."
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Cited by 25 (1 self)
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The qary ReedMuller codes RMq(u, m) of length n = qm are a generalization of ReedSolomon codes, which allow polynomials in m variables to encode the message. Using an idea of reducing the multivariate case to univariate case, randomized listdecoding algorithms for ReedMuller codes were given
On Berman's characterization of the ReedMuller codes
 Part I, J. Statist. Plann. Inference
, 1996
"... In a seminal paper, [3], Berman studied codes as ideals in a modular group algebra. In particular, he showed that the ReedMuller codes could be characterized as the powers of the radical in the group algebra, over F 2, of an ..."
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In a seminal paper, [3], Berman studied codes as ideals in a modular group algebra. In particular, he showed that the ReedMuller codes could be characterized as the powers of the radical in the group algebra, over F 2, of an
Redundancies of CorrectionCapabilityOptimized ReedMuller Codes
, 2008
"... This article is focused on some variations of ReedMuller codes that yield improvements to the rate for a prescribed decoding performance under the BerlekampMasseySakata algorithm with majority voting. Explicit formulas for the redundancies of the new codes are given. ..."
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This article is focused on some variations of ReedMuller codes that yield improvements to the rate for a prescribed decoding performance under the BerlekampMasseySakata algorithm with majority voting. Explicit formulas for the redundancies of the new codes are given.
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
Results 11  20
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1,444