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Physica A: Statistical Mechanics and its Applications, 2021
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Clarice Dias de Albuquerque +5 more
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Clarice Dias de Albuquerque +5 more
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MDS and near-MDS codes via twisted Reed–Solomon codes
Designs, Codes and Cryptography, 2022zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Junzhen Sui, Xiaomeng Zhu, Xueying Shi
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Construction of MDS twisted Reed–Solomon codes and LCD MDS codes
Designs, Codes and Cryptography, 2021The paper gives two constructions of twisted Reed-Solomon codes with two purposes. These are to provide new constructions, on the one hand, of MDS codes and, on the other hand, of linear complementary dual codes (LCD). LCD codes have acquired importance because of their interest in information protection against side-channel attacks and fault non ...
Hongwei Liu, Shengwei Liu
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IEEE Transactions on Information Theory, 1983
Summary: Maximum distance separable (MDS) convolutional codes are defined as the row space over \(F(D)\) of totally nonsingular polynomial matrices in the indeterminate \(D\). These codes may be used to transmit information on \(n\) parallel channels when a temporary or even an infinite break can occur in some of these channels.
Piret, Philippe, Krol, Thijs
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Summary: Maximum distance separable (MDS) convolutional codes are defined as the row space over \(F(D)\) of totally nonsingular polynomial matrices in the indeterminate \(D\). These codes may be used to transmit information on \(n\) parallel channels when a temporary or even an infinite break can occur in some of these channels.
Piret, Philippe, Krol, Thijs
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Designs, Codes and Cryptography, 1996
A linear \([n,k,d]\) code \(C\) over the finite field \(F_q\) is called almost maximum distance separable (AMDS for short) if its Singleton defect \(s(C) = n-k+1-d\) is one. A set of \(n\) points in the projective space \(PG(r,q)\) over \(F_q\) of dimension \(r\) is called \(n\)-track if every \(r\) of the points are not contained in a subspace of ...
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A linear \([n,k,d]\) code \(C\) over the finite field \(F_q\) is called almost maximum distance separable (AMDS for short) if its Singleton defect \(s(C) = n-k+1-d\) is one. A set of \(n\) points in the projective space \(PG(r,q)\) over \(F_q\) of dimension \(r\) is called \(n\)-track if every \(r\) of the points are not contained in a subspace of ...
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New Quantum MDS Codes From Negacyclic Codes
IEEE Transactions on Information Theory, 2013zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Kai, Xiaoshan, Zhu, Shixin
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Annals of Combinatorics, 2005
An MDS code over an alphabet of size \(q\) is a set of length \(n\) vectors with \(q^k\) elements where the minimum distance \(d\) satisfies \(d=n-k+1.\) Any MDS code satisfies the bound \(n \leq q+k-1.\) If equality is met in this bound the code is said to be of maximal length.
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An MDS code over an alphabet of size \(q\) is a set of length \(n\) vectors with \(q^k\) elements where the minimum distance \(d\) satisfies \(d=n-k+1.\) Any MDS code satisfies the bound \(n \leq q+k-1.\) If equality is met in this bound the code is said to be of maximal length.
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Journal of Geometry, 1993
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Karzel, Helmut, Maxson, Carl J.
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Karzel, Helmut, Maxson, Carl J.
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