Results 1 to 10 of about 90,302 (257)
Asymptotic Bound on Binary Self-Orthogonal Codes [PDF]
Science in China Series A: Mathematics, 2008 We present two constructions for binary self-orthogonal codes. It turns out that our constructions yield a constructive bound on binary self-orthogonal codes.
F. J. Macwilliams +8 more
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Symplectic QSD, LCD, and ACD Codes over a Non-Commutative Non-Unitary Ring of Order Nine [PDF]
EntropyWe introduce quasi self-dual (QSD), linear complementary dual (LCD), and additive complementary dual (ACD) codes for the symplectic inner product over a non-commutative non-unitary ring of order 9. We establish connections with symplectic–self-orthogonal
Sarra Manseri +3 more
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Quantum Block and Convolutional Codes from Self-orthogonal Product Codes [PDF]
Proceedings. International Symposium on Information Theory, 2005. ISIT 2005., 2005 We present a construction of self-orthogonal codes using product codes. From the resulting codes, one can construct both block quantum error-correcting codes and quantum convolutional codes. We show that from the examples of convolutional codes found, we
Grassl, Markus, Roetteler, Martin
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On Quasi-Cyclic Codes of Index 3 [PDF]
EntropyQuasi-cyclic codes of index 3 over finite fields are studied. We give a classification of such codes. Their duals with respect to the Euclidean and Hermitian inner products are investigated.
Kanat Abdukhalikov, Rasha M. Shat
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Some new QEC MDS codes with large minimum distance [PDF]
Scientific ReportsThe advancement of Quantum Error-Correcting (QEC) Maximum Distance Separable (MDS) codes holds substantial importance in practical applications, substantially augmenting the reliability and efficiency of quantum communication and computing.
Lanqiang Li +3 more
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New MDS Euclidean Self-Orthogonal Codes [PDF]
IEEE Transactions on Information Theory, 2021 In this paper, a criterion of MDS Euclidean self-orthogonal codes is presented. New MDS Euclidean self-dual codes and self-orthogonal codes are constructed via this criterion. In particular, among our constructions, for large square $q$, about $\frac{1}{8}\cdot q$ new MDS Euclidean (almost) self-dual codes over $\F_q$ can be produced.
Xiaolei Fang, Meiqing Liu, Jinquan Luo
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Ternary quantum codes constructed from extremal self-dual codes and self-orthogonal codes
AIMS Mathematics, 2022 In this paper, we consider S-chains of extremal self-dual and self-orthogonal codes and their applications in the construction of quantum codes. Then, by virtue of covering radius, we determine necessary conditions for linear codes to have subcodes with ...
Chaofeng Guan +4 more
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The mass formula for self-orthogonal and self-dual codes over a non-unitary commutative ring
AIMS Mathematics, 2023 In this paper, we establish a mass formula for self-orthogonal codes, quasi self-dual codes, and self-dual codes over commutative non-unital rings $ {{\mathit {I}_p}} = \left < a, b | pa = pb = 0, a^2 = b, ab = 0 \right > $, where $ p $ is an odd ...
Adel Alahmadi +2 more
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Linear codes resulting from finite group actions [PDF]
Transactions on Combinatorics, 2022 In this article, we use group action theory to define some important ternary linear codes. Some of these codes are self-orthogonal having a minimum distance achieving the lower bound in the previous records. Then, we define two new codes sharing the same
Driss Harzalla
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Construction of self-orthogonal Z2k-codes [PDF]
Designs, codes and cryptography, 2023 In this paper we give three constructions of cyclic self-orthogonal codes over Z_2^k, for k>=3, from Boolean functions on n variables.
Ban Martinović, Sara, Rukavina, Sanja
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