Results 261 to 270 of about 2,796,806 (297)
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IEEE Transactions on Information Theory, 1999
Summary: Let \(\mathbb{F}_q\) denote the finite field \(GF(q)\) and let \(b\) be a positive integer. MDS codes over the symbol alphabet \(\mathbb{F}^b_q\) are considered that are linear over \(\mathbb{F}_q\) and have sparse (``low-density'') parity-check and generator matrices over \(\mathbb{F}_q\) that are systematic over \(\mathbb{F}_q^b\).
Mario Blaum, Ron M. Roth
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Summary: Let \(\mathbb{F}_q\) denote the finite field \(GF(q)\) and let \(b\) be a positive integer. MDS codes over the symbol alphabet \(\mathbb{F}^b_q\) are considered that are linear over \(\mathbb{F}_q\) and have sparse (``low-density'') parity-check and generator matrices over \(\mathbb{F}_q\) that are systematic over \(\mathbb{F}_q^b\).
Mario Blaum, Ron M. Roth
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IEEE Transactions on Information Theory
Error-correcting codes are essential for ensuring fault tolerance in modern distributed data storage systems. However, in practice, factors such as the failure rates of storage devices can vary significantly over time, resulting in changes to the optimal
Haoming Shi, Weijun Fang, Yuan Gao
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Error-correcting codes are essential for ensuring fault tolerance in modern distributed data storage systems. However, in practice, factors such as the failure rates of storage devices can vary significantly over time, resulting in changes to the optimal
Haoming Shi, Weijun Fang, Yuan Gao
semanticscholar +1 more source
Constructions of Non-Generalized Reed–Solomon MDS Codes
IEEE Transactions on Information TheoryGeneralized Reed-Solomon codes form the most prominent class of maximum distance separable (MDS) codes, codes that are optimal in the sense that their minimum distance cannot be improved for a given length and code size.
Shengwei Liu, Hongwei Liu, F. Oggier
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On the Covering Radius of MDS Codes
IEEE Transactions on Information Theory, 2015For a linear maximum distance separable (MDS) code with redundancy $r$ , the covering radius is either $r$ or $r-1$ . However, for $r>3$ , few examples of $q$ -ary linear MDS codes with radius $r-1$ are known, including the Reed–Solomon codes with length $q+1$ . In this paper, for redundancies $r$ as large as
BARTOLI, DANIELE +2 more
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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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IEEE Transactions on Information Theory, 2011
New quantum maximum-distance-separable (MDS) codes with parameters [[q2 + 1, q2 -2d + 3, d]]q, where q=2t, t ≥ 1 and 3 ≤ d ≤ q+1 is an odd integer, are constructed in this paper.
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New quantum maximum-distance-separable (MDS) codes with parameters [[q2 + 1, q2 -2d + 3, d]]q, where q=2t, t ≥ 1 and 3 ≤ d ≤ q+1 is an odd integer, are constructed in this paper.
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2008 IEEE International Symposium on Information Theory, 2008
We consider the problem for which lengths a self-dual MDS code over Fq exists.We show that for q = 2m, there are self-dual MDS codes for all even lengths up to 2m. Furthermore, self-dual MDS codes of length q + 1 over Fq exist for all odd prime powers q. Additionally, we present some new self-dual MDS codes.
Markus Grassl, T. Aaron Gulliver
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We consider the problem for which lengths a self-dual MDS code over Fq exists.We show that for q = 2m, there are self-dual MDS codes for all even lengths up to 2m. Furthermore, self-dual MDS codes of length q + 1 over Fq exist for all odd prime powers q. Additionally, we present some new self-dual MDS codes.
Markus Grassl, T. Aaron Gulliver
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On generator matrices of MDS codes
IEEE Trans. Inf. Theory, 1985It is shown that the family of q-ary generalized Reed-Solomon codes is identical to the family of q-ary linear codes generated by matrices of the form [I\(| A]\), where I is the identity matrix, and A is a generalized Cauchy matrix. Using Cauchy matrices, a construction is shown of maximal triangular arrays over GF(q), which are constant along ...
Ron M. Roth, Gadiel Seroussi
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A condition for arcs and MDS codes
Designs, Codes and Cryptography, 2010zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Recursive MDS-Codes and Pseudogeometries
1999In [2,4] the notion of a recursive code was introduced and some constructions of recursive MDS codes were proposed. The main result was that for any q ∉ {2, 6} (except possibly q ∈ {14, 18, 26, 42}) there exists a recursive MDS-code in an alphabet of q elements of length 4 and combinatorial dimension 2 (i.e . a recursive [4, 2, 3]q-code).
Elena Couselo +3 more
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