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On the ReedMuller Codes
 Discrete Math
, 1992
"... We give a brief but complete account of all the essential facts concerning the ReedMuller and punctured ReedMuller codes. The treatment is new and includes an easy, direct proof of the fact that the punctured ReedMuller codes are the codes of the projective geometries over the binary field. We ..."
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Cited by 3 (0 self)
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We give a brief but complete account of all the essential facts concerning the ReedMuller and punctured ReedMuller codes. The treatment is new and includes an easy, direct proof of the fact that the punctured ReedMuller codes are the codes of the projective geometries over the binary field. We
Quantum ReedMuller Codes
, 1997
"... This paper presents a set of quantum ReedMuller codes which are typically 100 times more effective than existing quantum ReedMuller codes. The code parameters are [[n,k,d]] = [[2 m, ∑ r l=0 C(m,l) − ∑ m−r−1 l=0 C(m,l),2 m−r]] where 2r + 1> m> r. 1. ..."
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Cited by 2 (0 self)
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This paper presents a set of quantum ReedMuller codes which are typically 100 times more effective than existing quantum ReedMuller codes. The code parameters are [[n,k,d]] = [[2 m, ∑ r l=0 C(m,l) − ∑ m−r−1 l=0 C(m,l),2 m−r]] where 2r + 1> m> r. 1.
Reed.Muller Codes Associated to Projective Algebraic Varieties
, 2014
"... ReedMuller codes associated to projective algebraic varieties ..."
On trellis structures for ReedMuller codes
, 1999
"... We study trellises of ReedMuller codes from first principles. Our approach to local trellis behaviour seems to be new and yields amongst other things another proof of a result of Berger and Be'ery on the state complexity of ReedMuller codes. We give a general form of a minimalspan generato ..."
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Cited by 2 (1 self)
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We study trellises of ReedMuller codes from first principles. Our approach to local trellis behaviour seems to be new and yields amongst other things another proof of a result of Berger and Be'ery on the state complexity of ReedMuller codes. We give a general form of a minimal
Testing Reed Muller Codes
, 2003
"... A code is locally testable if there is a way to indicate with high probability that a vector is far enough from any codeword by accessing only a very small number of the vector’s bits. We show that the ReedMuller codes of constant order are locally testable. Specifically, we describe an efficient r ..."
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Cited by 2 (0 self)
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A code is locally testable if there is a way to indicate with high probability that a vector is far enough from any codeword by accessing only a very small number of the vector’s bits. We show that the ReedMuller codes of constant order are locally testable. Specifically, we describe an efficient
Quantum ReedMuller codes
 IEEE Trans. Inf. Theory
"... A set of quantum error correcting codes based on classical ReedMuller codes is described. The codes have parameters [[n,k,d]] = [[2 r, 2 r − C(r,t) − 2 ∑ t−1 i=0 C(r,i), 2t + 2 t−1]]. The study of quantum information is currently stimulating much interest. Most of the basic concepts of classical i ..."
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Cited by 20 (2 self)
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A set of quantum error correcting codes based on classical ReedMuller codes is described. The codes have parameters [[n,k,d]] = [[2 r, 2 r − C(r,t) − 2 ∑ t−1 i=0 C(r,i), 2t + 2 t−1]]. The study of quantum information is currently stimulating much interest. Most of the basic concepts of classical
Weighted ReedMuller codes revisited
, 2013
"... We consider weighted ReedMuller codes over point ensemble S1 × · · · × Sm where Si needs not be of the same size as Sj. For m = 2 we determine optimal weights and analyze in detail what is the impact of the ratio S1/S2  on the minimum distance. In conclusion the weighted ReedMuller code con ..."
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We consider weighted ReedMuller codes over point ensemble S1 × · · · × Sm where Si needs not be of the same size as Sj. For m = 2 we determine optimal weights and analyze in detail what is the impact of the ratio S1/S2  on the minimum distance. In conclusion the weighted ReedMuller code
Recursive decoding of ReedMuller codes
 Proceedings of IEEE International Symposium on Information Theory, ISIT’2000
, 2000
"... New soft and hard decision decoding algorithms are presented for general ReedMuller codes m r of length 2m and distance 2m r. We use Plotkin (u; u + v) construction and decompose code m m 1 n o r onto subblocks u 2 ..."
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Cited by 4 (1 self)
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New soft and hard decision decoding algorithms are presented for general ReedMuller codes m r of length 2m and distance 2m r. We use Plotkin (u; u + v) construction and decompose code m m 1 n o r onto subblocks u 2
Construction of Additive ReedMuller Codes ⋆
, 909
"... Abstract. The well known Plotkin construction is, in the current paper, generalized and used to yield new families of Z2Z4additive codes, whose length, dimension as well as minimum distance are studied. These new constructions enable us to obtain families of Z2Z4additive codes such that, under the ..."
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the Gray map, the corresponding binary codes have the same parameters and properties as the usual binary linear ReedMuller codes. Moreover, the first family is the usual binary linear ReedMuller family. Key Words: Z2Z4Additive codes, Plotkin construction, ReedMuller codes, Z2Z4linear codes.
ReedMuller Codes and Incidence Matrices
"... In this paper, we discuss ReedMuller codes using a settheoretic approach. We present a new basis of minimum weight codewords which correspond to subspaces of a fixed dimension of affine geometry over GF (2). A generator matrix in standard form is also given. ..."
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In this paper, we discuss ReedMuller codes using a settheoretic approach. We present a new basis of minimum weight codewords which correspond to subspaces of a fixed dimension of affine geometry over GF (2). A generator matrix in standard form is also given.
Results 1  10
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