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On the Classification of Self-dual -Codes
2009A classification of self-dual -codes of modest lengths is known for small k . For k = 4,6,8,9 and 10, the classification of self-dual -codes is extended to lengths 19,12,12,12 and 10, respectively, by considering k -frames of unimodular lattices.
Masaaki Harada, Akihiro Munemasa
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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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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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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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Self-Dual Codes and Self-Dual Designs
1990We construct self-orthogonal binary codes from projective 2 - (v, k, λ) designs with a polarity, k odd, and λ even. We give arithmetic conditions on the parameters of the design to obtain self-dual or doubly even self-dual codes. Non existence results in the latter case are obtained from rationality conditions of certain strongly regular graphs.
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Self-dual extended cyclic codes
Applicable Algebra in Engineering, Communication and Computing, 2005Using representation theoretical and number theoretical methods the authors investigate self-dual group codes and their extensions. The existence of a self-dual extended group code heavily depends on a particular structure of the group algebra which is defined by the number theoretic properties of the parameters of this algebra.
Conchita Martínez-Pérez +1 more
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Construction of cubic self-dual codes
2009 IEEE International Symposium on Information Theory, 2009We present a building-up construction method for quasi-cyclic self-dual codes over finite fields. By using this, we give cubic (i.e., l-quasi-cyclic codes of length 3l) self-dual codes over various finite fields, which are optimal or have the best known parameters.
Sunghyu Han +3 more
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IEEE Transactions on Information Theory, 2008
In this correspondence, we construct new self-dual codes over F4, F5, F7 with larger minimum weights than the previously known self-dual codes, using construction methods based on circulant and negacirculant matrices. In particular, a self-dual [36,18,13] code over F7 is constructed which has a larger minimum weight than the previously known [36,18 ...
T. Aaron Gulliver, Masaaki Harada
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In this correspondence, we construct new self-dual codes over F4, F5, F7 with larger minimum weights than the previously known self-dual codes, using construction methods based on circulant and negacirculant matrices. In particular, a self-dual [36,18,13] code over F7 is constructed which has a larger minimum weight than the previously known [36,18 ...
T. Aaron Gulliver, Masaaki Harada
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A systematic construction of self-dual codes
IEEE Transactions on Information Theory, 2003A new coding construction scheme of block codes using short base codes and permutations that enables the construction of binary self-dual codes is presented in Cadic et al. (2001) and Carlach et al. (1999, 2000). The scheme leads to doubly-even (resp,. singly-even) self-dual codes provided the base code is a doubly-even self-dual code and the number of
Jean-Claude Carlach, Ayoub Otmani
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On Binary Self-Dual Codes With Automorphisms
IEEE Transactions on Information Theory, 2008In this correspondence, we present some results concerning a decomposition of binary self-dual codes possessing an automorphism of certain type. Two applications are given. The first one is the classification of all extremal doubly even self-dual codes of length having an automorphism of order .
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