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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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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,
Jon-Lark Kim, 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,
Jon-Lark Kim, Yoonjin Lee
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Finite Fields and Their Applications, 2022
For a linear code of parameters \([n, k, d],\) the Singleton bound says that \(d \leq n-k+1.\) If this equality holds, i.e., \(d =n-k+1,\) then the code is called a maximum distance separable (MDS) code. If \(d =n-k,\) then the code is called an almost MDS (AMDS for short) code.
Xiaojun Geng +3 more
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For a linear code of parameters \([n, k, d],\) the Singleton bound says that \(d \leq n-k+1.\) If this equality holds, i.e., \(d =n-k+1,\) then the code is called a maximum distance separable (MDS) code. If \(d =n-k,\) then the code is called an almost MDS (AMDS for short) code.
Xiaojun Geng +3 more
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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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2000
We investigate the question when a cyclic code is maximum distance separable (MDS). For codes of (co-)dimension 3, this question is related to permutation properties of the polynomial (x b -1)/(x-1) for a certain b. Using results on these polynomials we prove that over fields of odd characteristic the only MDS cyclic codes of dimension 3 are the Reed ...
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We investigate the question when a cyclic code is maximum distance separable (MDS). For codes of (co-)dimension 3, this question is related to permutation properties of the polynomial (x b -1)/(x-1) for a certain b. Using results on these polynomials we prove that over fields of odd characteristic the only MDS cyclic codes of dimension 3 are the Reed ...
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Journal of Geometry, 1993
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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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Column Twisted Reed-Solomon Codes as MDS Codes
IEEE Transactions on Information TheoryIn 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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On the Stopping Redundancy of MDS Codes
2006 IEEE International Symposium on Information Theory, 2006The stopping redundancy of a linear code is defined as the minimum number of rows in its parity-check matrix such that the smallest stopping sets have size equal to the minimum distance of the code. We derive new upper bounds on the stopping redundancy of maximum distance separable (MDS) codes, and show how they improve upon previously known results ...
Junsheng Han, Paul H. Siegel
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On MDS Convertible Codes in the Merge Regime
IEEE Transactions on Information TheoryIn large-scale distributed storage systems, erasure coding is employed to ensure reliability against disk failures. Recent work by Kadekodi et al. demonstrates that adapting code parameters to varying disk failure rates can lead to significant storage ...
Vinayak Ramkumar +5 more
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On the Reliability of Information Retrieval from MDS Coded Data in DNA Storage
International Symposium on Information TheoryThis work presents a theoretical analysis of the probability of successfully retrieving data encoded with MDS codes (e.g., Reed-Solomon codes) in DNA storage systems.
Serge Kas Hanna
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