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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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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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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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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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Construction of self-dual matrix codes
Designs, Codes and Cryptography, 2020zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Lucky Galvez, Jon-Lark Kim
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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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Gleason's theorem on self-dual codes
IEEE Transactions on Information Theory, 1972The weight enumerator of a code \(C\) is the polynomial \[ W(x,y) = \sum_{r=0}^n A_rx^{n-r}y^r, \] where \(n\) is the block length and \(A_r\) is the number of codewords of weight \(r\). A theorem of \textit{A. M. Gleason} [Actes Congr. Int. Math., Nice 1970, Vol.
Elwyn R. Berlekamp +2 more
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2016
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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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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1998
In this chapter, we shall present some fundamental study on relatively self-dual codes over a finite commutative ring. Section 1.1 is devoted to the basic definitions and properties of such codes. In Section 1.2, we shall present our gluing technique for constructing relatively self-dual codes.
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In this chapter, we shall present some fundamental study on relatively self-dual codes over a finite commutative ring. Section 1.1 is devoted to the basic definitions and properties of such codes. In Section 1.2, we shall present our gluing technique for constructing relatively self-dual codes.
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