Results 241 to 250 of about 35,611 (258)
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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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Constacyclic Codes and Some New Quantum MDS Codes
IEEE Transactions on Information Theory, 2014zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Kai, Xiaoshan, Zhu, Shixin, Li, Ping
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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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International Symposium onInformation Theory, 2004. ISIT 2004. Proceedings., 2004
We construct maximum distance separable quantum error-correcting codes. The codes are defined over q-dimensional quantum systems, where q is any prime power. The construction yields quantum MDS codes of length up to q+1 for all possible dimensions and some quantum MDS codes of length up to q2+1.
Rötteler, M., Grassl, M., Beth, T.
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We construct maximum distance separable quantum error-correcting codes. The codes are defined over q-dimensional quantum systems, where q is any prime power. The construction yields quantum MDS codes of length up to q+1 for all possible dimensions and some quantum MDS codes of length up to q2+1.
Rötteler, M., Grassl, M., Beth, T.
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