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Column Twisted Reed-Solomon Codes as MDS Codes
arXiv.orgIn this paper, we study column twisted Reed-Solomon(TRS) codes. We establish some sufficient conditions for these codes to be MDS and show that the dimension of their Schur square codes is $2k$.
Wei Liu +3 more
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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
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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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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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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
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Dodunekov, Stefan, Landgev, Ivan
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zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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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Short Code: An Efficient RAID-6 MDS Code for Optimizing Degraded Reads and Partial Stripe Writes
IEEE transactions on computers, 2017Yingxun Fu +4 more
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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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HV Code: An All-Around MDS Code to Improve Efficiency and Reliability of RAID-6 Systems
2014 44th Annual IEEE/IFIP International Conference on Dependable Systems and Networks, 2014Zhirong Shen, J. Shu
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