Results 1 to 10 of about 56,494 (184)
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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Improved Spectral Bound for Quasi-Cyclic Codes [PDF]
IEEE Transactions on Information Theory, 2023 Spectral bounds form a powerful tool to estimate the minimum distances of quasi-cyclic codes. They generalize the defining set bounds of cyclic codes to those of quasi-cyclic codes.
Gaojun Luo +3 more
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Lower Bounds for Quasi-Cyclic Codes and New Binary Quantum Codes
Symmetry, 2023 This paper considers three kinds of quasi-cyclic codes of index two with one generator or two generators and their applications in quantum code construction. In accordance with the algebraic structure of linear codes, we determine the lower bounds of the
Chao Du, Zhi Ma, Chaofeng Guan
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Quasi-cyclic codes of index 2 [PDF]
Discrete MathematicsWe study quasi-cyclic codes of index 2 over finite fields. We give a classification of such codes. Their duals with respect to the Euclidean, symplectic and Hermitian inner products are investigated. We describe self-orthogonal and dual-containing codes.
K. Abdukhalikov +2 more
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New Binary Quantum Codes Derived From One-Generator Quasi-Cyclic Codes
IEEE Access, 2019 In this paper, we consider a family of one-generator quasi-cyclic (QC) codes and their applications in quantum codes construction. We give a sufficient condition for one-generator QC codes to be self-orthogonal with respect to the symplectic inner ...
Jingjie Lv, Ruihu Li, Junli Wang
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On quasi-cyclic codes and traces of codes
Lietuvos Matematikos Rinkinys, 2004 There is not abstract.
Gintaras Skersys
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On Gray Images of Cyclic and Self-Orthogonal Codes over
EntropyLet p be a prime with p∉{2,5} and let q=pm. This paper studies cyclic and self-orthogonal linear codes of length n over the finite local non-Frobenius ring Rp,u,v=Fq+uFq+vFq, u2=v2=uv=vu=0.
Sami H. Saif, Alhanouf Ali Alhomaidhi
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Linking Reversed and Dual Codes of Quasi-Cyclic Codes
IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences, 2022 SUMMARY It is known that quasi-cyclic (QC) codes over the finite field F 𝑞 correspond to certain F 𝑞 [ 𝑥 ] -modules. A QC code C is specified by a generator polynomial matrix 𝐺 whose rows generate C as an F 𝑞 [ 𝑥 ] -module.
R. T. Eldin, H. Matsui
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Quasi-Cyclic Codes Via Unfolded Cyclic Codes and Their Reversibility
IEEE Access, 2019 The finite field $\mathbb {F}_{q^\ell }$ of $q^\ell $ elements contains $\mathbb {F}_{q}$ as a subfield. If $\theta \in \mathbb {F}_{q^\ell }$ is of degree $\ell $ over $\mathbb {F}_{q}$ , it can be used to unfold elements of $\mathbb {F}_{q^\
Ramy Taki Eldin, Hajime Matsui
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Symplectic Self-Orthogonal Quasi-Cyclic Codes
IEEE Transactions on Information Theory, 2022 In this paper, we establish the necessary and sufficient conditions for quasi-cyclic (QC) codes with index even to be symplectic self-orthogonal. Subsequently, we present the lower and upper bounds on the minimum symplectic distances of a class of 1 ...
Chaofeng Guan, Ruihu Li, Zhi Ma
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