Results 21 to 30 of about 374,444 (257)
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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Classification of quaternary Hermitian self-dual codes of length 20 [PDF]
, 2010 A classification of quaternary Hermitian self-dual codes of length 20 is given. Using this classification, a classification of extremal quaternary Hermitian self-dual codes of length 22 is also given.Comment: 9 pages.
Harada, Masaaki, Munemasa, Akihiro
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SHADOW OPTIMAL SELF-DUAL CODES
Kyushu Journal of Mathematics, 1999 This paper considers binary linear self-dual codes. An optimal self-dual code has the highest minimum weight for the given length. Shadow codes were previously introduced by \textit{J. H. Conway} and \textit{N. J. A. Sloane} [IEEE Trans. Inf. Theory 36, 1319-1333 (1990; Zbl 0713.94016)].
Dougherty, Steven T., Harada, Masaaki
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Construction of isodual codes from polycirculant matrices
, 2020 Double polycirculant codes are introduced here as a generalization of double circulant codes. When the matrix of the polyshift is a companion matrix of a trinomial, we show that such a code is isodual, hence formally self-dual.
Shi, Minjia, Sole, Patrick, Xu, Li
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Transitive and self-dual codes attaining the Tsfasman-Vladut-Zink bound [PDF]
, 2005 A major problem in coding theory is the question of whether the class of cyclic codes is asymptotically good. In this correspondence-as a generalization of cyclic codes-the notion of transitive codes is introduced (see Definition 1.4 in Section I), and ...
Stichtenoth, Henning
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Extended binary Golay codes by a group algebra of one group
Науковий вісник Ужгородського університету. Серія: Математика і інформатика, 2020 Extended binary Golay codes are examples of extreme binary self-dual codes of Type II (linear binary self-dual codes with Hamming distance between arbitrary codewords which are multiples of 4 that has the highest possible minimum Hamming distance among ...
М. Ю. Бортош +1 more
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Narain CFTs and error-correcting codes on finite fields
Journal of High Energy Physics, 2022 We construct Narain CFTs from self-dual codes on the finite field F p through even self-dual lattices for any prime p > 2. Using this correspondence, we can relate the spectral gap and the partition function of the CFT to the error correction capability ...
Shinichiro Yahagi
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Mass Formula for Self-Orthogonal and Self-Dual Codes over Non-Unital Rings of Order Four
Mathematics, 2023 We study the structure of self-orthogonal and self-dual codes over two non-unital rings of order four, namely, the commutative ring I=a,b|2a=2b=0,a2=b,ab=0 and the noncommutative ring E=a,b|2a=2b=0,a2=a,b2=b,ab=a,ba=b.
Adel Alahmadi +4 more
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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.
Alahmadi, Adel +2 more
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Additive Self-Dual Codes over GF(4) with Minimal Shadow
Information, 2018 We define additive self-dual codes over G F ( 4 ) with minimal shadow, and we prove ...
Sunghyu Han
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