Results 241 to 250 of about 533,291 (281)
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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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A class of subfield codes of linear codes and their duals
Cryptography and Communications, 2020zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Xiaoqiang Wang 0001 +2 more
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On Euclidean self-dual codes and isometry codes
Applicable Algebra in Engineering, Communication and Computing, 2020This work introduces new methods and algorithms to construct Euclidean self-dual codes over large finite fields. A new algorithm to construct orthogonal matrices is presented and this algorithm is applied to construct self-dual codes over finite fields. The orthogonal group of index \(n\) over a \(\mathbb{F}_q\) is defined by \(\mathcal{O}_n(q)=\{A \in
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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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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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Dual transform and projective self-dual codes
Advances in Mathematics of CommunicationsThe authors study linear codes using the projective dual transform. Their approach is to represent codes by a characteristic vector and the characteristic vector of the projective dual is obtained as a product of a special matrix by the characteristic vector of the input code.
Iliya Bouyukliev, Stefka Bouyuklieva
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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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On the dual of quaternary goethals code
Applied Mathematics-A Journal of Chinese Universities, 2001\textit{A. Hammons}, \textit{P. V. Kumar}, \textit{A. Calderbank}, \textit{N. J. A. Sloane} and \textit{P. Solé} [IEEE Trans. Inf. Theory 40, 301-319 (1994; Zbl 0811.94039)] described how Kerdock, Preparata and Goethals codes can be viewed as binary images of certain quaternary \(\mathbb{Z}_4\)-linear codes. This paper studies more extensively the dual
Cui, Jie, Pei, Junying
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On Dual Relationships of Secrecy Codes
2018 56th Annual Allerton Conference on Communication, Control, and Computing (Allerton), 2018We investigate properties of finite blocklength codes and their duals when used for coset coding over the binary erasure wiretap channel (BEWC). We identify sufficient conditions, related to the ranks of sub-matrices of a generator matrix that codes may satisfy to achieve the maximum equivocation among all codes with given blocklength and dimension ...
Harrison, Willie, Bloch, Matthieu
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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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