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Extremal binary self-dual codes
IEEE Transactions on Information Theory, 1997Summary: In this correspondence, we investigate binary extremal self-dual codes. Numerous extremal self-dual codes and interesting self-dual codes with minimum weight \(d=14\) and 16 are constructed. In particular, the first extremal Type I \([86, 43, 16]\) code and new extremal self-dual codes with weight enumerators which were not previously known to
Dougherty, Steven T. +2 more
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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.
Babai, L., Oral, H., Phelps, K. T.
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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.
Babai, L., Oral, H., Phelps, K. T.
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2017
In this chapter, we describe self-dual codes over Frobenius rings. We give constructions of self-dual codes over any Frobenius ring. We describe connections to unimodular lattices, binary self-dual codes and to designs. We also describe linear complementary dual codes and make a new definition of a broad generalization encompassing both self-dual and ...
MinJia Shi, Adel Alahmadi, Patrick Sole
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In this chapter, we describe self-dual codes over Frobenius rings. We give constructions of self-dual codes over any Frobenius ring. We describe connections to unimodular lattices, binary self-dual codes and to designs. We also describe linear complementary dual codes and make a new definition of a broad generalization encompassing both self-dual and ...
MinJia Shi, Adel Alahmadi, Patrick Sole
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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.
Dougherty, Steven T. +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.
Dougherty, Steven T. +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,
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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1988
A linear code C is called self-dual if C = C⊥. Clearly the rate of such a code is 1/2. Many authors have studied such codes and discovered interesting connections with invariant theory and with lattice sphere packings (cf. Mac Williams and Sloane, 1977, Ch. 19). Recently there has been interest in geometric Goppa codes that are self-dual.
Jacobus H. van Lint, Gerard van der Geer
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A linear code C is called self-dual if C = C⊥. Clearly the rate of such a code is 1/2. Many authors have studied such codes and discovered interesting connections with invariant theory and with lattice sphere packings (cf. Mac Williams and Sloane, 1977, Ch. 19). Recently there has been interest in geometric Goppa codes that are self-dual.
Jacobus H. van Lint, Gerard van der Geer
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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
Sloane, N. J. A., Thompson, J. G.
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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
Sloane, N. J. A., Thompson, J. G.
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Self-Dual Codes Over Chain Rings
Mathematics in Computer Science, 2019zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Eisenbarth, Simon, Nebe, Gabriele
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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.
Dougherty, Steven T. +2 more
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