Results 1 - 10 of 1,444

On the Reed-Muller Codes

by E. F. Assmus, Jr. - Discrete Math , 1992
"... We give a brief but complete account of all the essential facts concerning the ReedMuller and punctured Reed-Muller codes. The treatment is new and includes an easy, direct proof of the fact that the punctured Reed-Muller codes are the codes of the projective geometries over the binary field. We ..."
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We give a brief but complete account of all the essential facts concerning the ReedMuller and punctured Reed-Muller codes. The treatment is new and includes an easy, direct proof of the fact that the punctured Reed-Muller codes are the codes of the projective geometries over the binary field. We

Quantum Reed-Muller Codes

by Lin Zhang, Ian Fuss , 1997
"... This paper presents a set of quantum Reed-Muller codes which are typically 100 times more effective than existing quantum Reed-Muller 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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This paper presents a set of quantum Reed-Muller codes which are typically 100 times more effective than existing quantum Reed-Muller 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

by unknown authors , 2014
"... Reed-Muller codes associated to projective algebraic varieties ..."
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Reed-Muller codes associated to projective algebraic varieties

On trellis structures for Reed-Muller codes

by Tim Blackmore, Graham Norton , 1999
"... We study trellises of Reed-Muller 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 Reed--Muller codes. We give a general form of a minimal--span generato ..."
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We study trellises of Reed-Muller 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 Reed--Muller codes. We give a general form of a minimal

Testing Reed Muller Codes

by Noga Alon, Tali Kaufman, Michael Krivelevich, Simon Litsyn, Dana Ron , 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 Reed-Muller codes of constant order are locally testable. Specifically, we describe an efficient r ..."
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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 Reed-Muller codes of constant order are locally testable. Specifically, we describe an efficient

Quantum Reed-Muller codes

by A. M. Steane - IEEE Trans. Inf. Theory
"... A set of quantum error correcting codes based on classical Reed-Muller 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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A set of quantum error correcting codes based on classical Reed-Muller 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 Reed-Muller codes revisited

by Olav Geil, Casper Thomsen , 2013
"... We consider weighted Reed-Muller 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 Reed-Muller code con ..."
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We consider weighted Reed-Muller 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 Reed-Muller code

Recursive decoding of Reed-Muller codes

by Ilya Dumer - Proceedings of IEEE International Symposium on Information Theory, ISIT’2000 , 2000
"... New soft- and hard decision decoding algorithms are presented for general Reed-Muller 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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New soft- and hard decision decoding algorithms are presented for general Reed-Muller 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 Reed-Muller Codes ⋆

by J. Pujol, J. Rifà, L. Ronquillo , 909
"... Abstract. The well known Plotkin construction is, in the current paper, generalized and used to yield new families of Z2Z4-additive codes, whose length, dimension as well as minimum distance are studied. These new constructions enable us to obtain families of Z2Z4-additive 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 Reed-Muller codes. Moreover, the first family is the usual binary linear Reed-Muller family. Key Words: Z2Z4-Additive codes, Plotkin construction, Reed-Muller codes, Z2Z4-linear codes.

Reed-Muller Codes and Incidence Matrices

by M. Karimi Behbahani G. B. Khosrovshahi, B. Tayfeh-Rezaie
"... In this paper, we discuss Reed-Muller codes using a set-theoretic 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 Reed-Muller codes using a set-theoretic 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 of 1,444