Results 21 to 30 of about 5,817,872 (291)
Linear programming bounds for doubly-even self-dual codes [PDF]
, 1997 Using a variant of linear programming method we derive a new upper bound on the minimum distance d of doubly-even self-dual codes of length n. Asymptotically, for n growing, it gives d/n
Krasikov, I +4 more
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An improved upper bound on the minimum distance of doubly-even self-dual codes [PDF]
, 2000 We derive a new upper bound on the minimum distance d of doubly-even self-dual codes of length n. Asymptotically, for n growing, it gives limn→∞ sup d/n
Krasikov, I, Litsyn, S
core +1 more source
On self-dual affine-invariant codes [PDF]
, 1993 An extended cyclic code of length 2m over GF(2) cannot be self-dual for even m. For odd m, the Redd-Muller code [2m, 2m-1, 2(m+1)/2] is affine-invariant and self-dual and it is the only such code for m = 3 or 5.
Levy-Dit-Vehel, Françoise +1 more
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Near-Extremal Type I Self-Dual Codes with Minimal Shadow over GF(2) and GF(4)
Information, 2018 Binary self-dual codes and additive self-dual codes over GF(4) contain common points. Both have Type I codes and Type II codes, as well as shadow codes. In this paper, we provide a comprehensive description of extremal and near-extremal Type I codes over
Sunghyu Han
doaj +1 more source
Advances in Mathematics of Communications, 2016 Improved exposition according to the referees ...
Gabriele Nebe, Wolfgang Willems
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On self-dual double circulant codes [PDF]
Designs, Codes and Cryptography, 2017 Self-dual double circulant codes of odd dimension are shown to be dihedral in even characteristic and consta-dihedral in odd characteristic. Exact counting formulae are derived for them and used to show they contain families of codes with relative distance satisfying a modified Gilbert-Varshamov bound.
Adel Alahmadi +2 more
openaire +7 more sources
Self-Dual Cyclic Codes Over M2(ℤ4)
Discussiones Mathematicae - General Algebra and Applications, 2022 In this paper, we study the structure of cyclic codes overM2(ℤ4) (the matrix ring of matrices of order 2 over ℤ4), which is perhaps the first time that the ring is considered as a code alphabet.
Bhowmick Sanjit +3 more
doaj +1 more source
Hermitian Self-Dual Abelian Codes [PDF]
IEEE Transactions on Information Theory, 2014 Hermitian self-dual abelian codes in a group ring Fq2[G], where Fq2 is a finite field of order q2 and G is a finite abelian group, are studied. Using the well-known discrete Fourier transform decomposition for a semisimple group ring, a characterization of Hermitian self-dual abelian codes in Fq2[G] is given, together with an alternative proof of ...
Somphong Jitman, San Ling, Patrick Solé
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Gottesman-Kitaev-Preskill codes: A lattice perspective [PDF]
Quantum, 2022 We examine general Gottesman-Kitaev-Preskill (GKP) codes for continuous-variable quantum error correction, including concatenated GKP codes, through the lens of lattice theory, in order to better understand the structure of this class of stabilizer codes.
Jonathan Conrad +2 more
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On the enumeration of self-dual codes
Journal of Combinatorial Theory, Series A, 1980 AbstractWe give the complete classification of all binary, self-dual, doubly-even (32, 16) codes. There are 85 non-equivalent, self-dual, doubly-even (32, 16) codes. Five of these have minimum weight 8, namely, a quadratic residue code and a Reed-Muller code, and three new codes.
John H. Conway, Vera Pless
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