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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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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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International Symposium onInformation Theory, 2004. ISIT 2004. Proceedings., 2004
In this paper we develop a complete generalization of the building-up method [J.-L. Kim, (2001)] for the Euclidean and Hermitian self-dual codes over finite fields GF(q). Using this method we construct many new Euclidean and Hermitian self-dual MDS (or near MDS) codes of length up to 12 over various finite fields GF(q), where q=8, 9, 16, 25, 32, 41, 49,
null Jon-Lark Kim, null Yoonjin Lee
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In this paper we develop a complete generalization of the building-up method [J.-L. Kim, (2001)] for the Euclidean and Hermitian self-dual codes over finite fields GF(q). Using this method we construct many new Euclidean and Hermitian self-dual MDS (or near MDS) codes of length up to 12 over various finite fields GF(q), where q=8, 9, 16, 25, 32, 41, 49,
null Jon-Lark Kim, null Yoonjin Lee
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IEEE Transactions on Information Theory, 2014
In this paper, we extend the concept of maximum-distance separable (MDS) array codes to a larger class of codes, where the array columns contain a variable number of data and parity symbols and the codewords cannot be arranged, in general, in a regular array structure with equal column length.
Filippo Tosato, Magnus Sandell
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In this paper, we extend the concept of maximum-distance separable (MDS) array codes to a larger class of codes, where the array columns contain a variable number of data and parity symbols and the codewords cannot be arranged, in general, in a regular array structure with equal column length.
Filippo Tosato, Magnus Sandell
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Proceedings of 1994 IEEE International Symposium on Information Theory, 1995
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Dodunekov, Stefan, Landgev, Ivan
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Dodunekov, Stefan, Landgev, Ivan
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