Results 251 to 260 of about 5,817,872 (291)
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SIAM Journal on Discrete Mathematics, 1994
Summary: The authors present a construction of binary self-dual codes from Eulerian graphs and establish that the code will be indecomposable if and only if the vertices of degree 2 are not a cutset of the graph. The construction is used to establish that every finite group is isomorphic to the automorphism group of some self-dual code.
László Babai +2 more
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Summary: The authors present a construction of binary self-dual codes from Eulerian graphs and establish that the code will be indecomposable if and only if the vertices of degree 2 are not a cutset of the graph. The construction is used to establish that every finite group is isomorphic to the automorphism group of some self-dual code.
László Babai +2 more
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Applicable Algebra in Engineering, Communication and Computing, 2020
In this paper, the authors define a self-dual code over a finite abelian group in terms of an arbitrary duality on the ambient space. They determine when additive self-dual codes exist over abelian groups for any duality and describe various constructions for these codes.
Steven T. Dougherty +2 more
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In this paper, the authors define a self-dual code over a finite abelian group in terms of an arbitrary duality on the ambient space. They determine when additive self-dual codes exist over abelian groups for any duality and describe various constructions for these codes.
Steven T. Dougherty +2 more
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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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Construction of Self-Dual Codes
IEEE Transactions on Information Theory, 2008Construction methods for self-dual codes are given. By using these methods some new extremal self-dual [66, 33, 12] and [68, 34, 12] codes are obtained.
Han-Ping Tsai +4 more
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IEEE Transactions on Information Theory, 1983
It is shown that if the automorphism group of a binary self-dual code satisfies a certain condition then the code contains words of weight congruent to 2 modulo 4 . In particular, no cyclic binary self-dual code can have all its weights divisible by four. The number of cyclic binary self-dual codes of length n is determined, and the shortest nontrivial
Neil J. A. Sloane, John G. Thompson 0001
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It is shown that if the automorphism group of a binary self-dual code satisfies a certain condition then the code contains words of weight congruent to 2 modulo 4 . In particular, no cyclic binary self-dual code can have all its weights divisible by four. The number of cyclic binary self-dual codes of length n is determined, and the shortest nontrivial
Neil J. A. Sloane, John G. Thompson 0001
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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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Constructions of self-dual codes and formally self-dual codes over rings
Applicable Algebra in Engineering, Communication and Computing, 2016zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Steven T. Dougherty +2 more
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Mathematical Journal of Okayama University, 1995
The authors investigate the existence of new extremal self dual codes. In orderto construct such codes, they present general methods for constructing self-dual codes and they obtain extremal self-dual codes having weight enumerators for which extremal codes were not previously known to exist, using some matrices.
Harada, Masaaki, Kimura, Hiroshi
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The authors investigate the existence of new extremal self dual codes. In orderto construct such codes, they present general methods for constructing self-dual codes and they obtain extremal self-dual codes having weight enumerators for which extremal codes were not previously known to exist, using some matrices.
Harada, Masaaki, Kimura, Hiroshi
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Weight enumerators of self-dual codes
IEEE Transactions on Information Theory, 1991Some construction techniques for self-dual codes are investigated, and the authors construct a singly-even self-dual (48,24,10)-code with a weight enumerator that was not known to be attainable. It is shown that there exists a singly-even self-dual code C' of length n=48 and minimum weight d=10 whose weight enumerator is prescribed in the work of J.H ...
Richard A. Brualdi, Vera Pless
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On designs and formally self-dual codes
Designs, Codes and Cryptography, 1994A code \(C\) is formally self-dual if \(C\) has the same weight distribution as its dual code \(C^ \perp\). The authors study binary formally self- dual codes and demonstrate that the class of such codes contains codes that have greater minimum distance than any self-dual code with the same parameters. A strengthening of the Assmus-Mattson theorem that
George T. Kennedy, Vera Pless
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