Results 21 to 30 of about 640,608 (278)
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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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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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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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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On the Problem of the Existence of a Square Matrix U Such That UUT = −I over Zpm
Information, 2017 Building-up construction is one of several methods for constructing self-dual codes. Recently, a new building-up construction method has been developed by S.
Sunghyu Han
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, 2002 Self-dual codes are important because many of the best codes known are of this type and they have a rich mathematical theory. Topics covered in this survey include codes over F_2, F_3, F_4, F_q, Z_4, Z_m, shadow codes, weight enumerators, Gleason-Pierce theorem, invariant theory, Gleason theorems, bounds, mass formulae, enumeration, extremal codes ...
Rains, E. M., Sloane, N. J. A.
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Reversible Self-Dual Codes over Finite Field
Cauchy: Jurnal Matematika Murni dan AplikasiReversible self-dual code is a linear code which combine the properties from self-dual code and reversible code. Previous research shows that reversible self-dual codes have only been developed over field of order 2 and order 4.
Ardi Nur Hidayat +2 more
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Some results on free Euclidean self-dual codes over F2+vF2
Sakarya Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 2019 In thispaper, free Euclidean self-dual codes over the ring F2+ v F2 with v2=vof order 4 are considered. A necessary andsufficient condition for the form of the generator matrix of a free Euclideanself-dual code is given.
Refia Aksoy, Fatma Çalışkan
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On McEliece-Type Cryptosystems Using Self-Dual Codes With Large Minimum Weight
IEEE Access, 2023 One of the Round 3 Finalists in the NIST post-quantum cryptography call is the Classic McEliece cryptosystem. Although it is one of the most secure cryptosystems, the large size of its public key remains a practical limitation. In this work, we propose a
Luca Mariot +2 more
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An Enumeration of the Equivalence Classes of Self-Dual Matrix Codes
, 2015 As a result of their applications in network coding, space-time coding, and coding for criss-cross errors, matrix codes have garnered significant attention; in various contexts, these codes have also been termed rank-metric codes, space-time codes over ...
Morrison, Katherine
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