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Generalized GM-MDS: Polynomial Codes Are Higher Order MDS
IEEE Transactions on Information Theory, 2023The GM-MDS theorem, conjectured by Dau-Song-Dong-Yuen and proved by Lovett and Yildiz-Hassibi, shows that the generator matrices of Reed-Solomon codes can attain every possible configuration of zeros for an MDS code.
Joshua Brakensiek, Manik Dhar, S. Gopi
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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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zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Karzel, Helmut, Maxson, Carl J.
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IEEE Transactions on Information Theory, 2021
Let $q=p^{e}$ be a prime power and $\ell $ be an integer with $0\leq \ell \leq e-1$ . The $\ell $ -Galois hull of classical linear codes is a generalization of the Euclidean hull and Hermitian hull.
Meng Cao
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Let $q=p^{e}$ be a prime power and $\ell $ be an integer with $0\leq \ell \leq e-1$ . The $\ell $ -Galois hull of classical linear codes is a generalization of the Euclidean hull and Hermitian hull.
Meng Cao
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Non-Reed-Solomon Type Cyclic MDS Codes
IEEE Transactions on Information TheoryAs cyclic codes and maximum distance separable (MDS) codes, cyclic MDS codes have very nice structures and properties, which have been intensively investigated in literature due to their theoretical interest and practical importance.
Fagang Li +3 more
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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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