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Quasi-cyclic and generalized quasi-cyclic codes and uniqueness of their generators

Discrete Mathematics, Algorithms and Applications, 2022
In this paper, we use a novel approach to describe generator polynomials of quasi-cyclic (QC) and generalized QC (GQC) codes over finite fields. Our study of QC- and GQC-codes will be general and not only restricted to one-generator codes.
T. Abualrub, P. Seneviratne
semanticscholar   +2 more sources

Symplectic Self-Orthogonal Quasi-Cyclic Codes

open access: yesIEEE 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
semanticscholar   +3 more sources

Quasi-cyclic codes of index 2

open access: yesDiscrete Mathematics
We 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
semanticscholar   +3 more sources

On construction of quantum codes with dual-containing quasi-cyclic codes

Quantum Information Processing, 2022
One of the main objectives of quantum error-correction theory is to construct quantum codes with optimal parameters and properties. In this paper, we propose a class of 2-generator quasi-cyclic codes and study their applications in the construction of ...
Chaofeng Guan   +4 more
semanticscholar   +1 more source

An Explicit Construction of Quantum Stabilizer Codes From Quasi-Cyclic Codes

IEEE Communications Letters, 2020
In this short letter, our main objective is to construct good quantum stabilizer codes over small fields, which have a more potential possibility to be employed in actual quantum processors.
Jingjie Lv, Ruihu Li, Junli Wang
semanticscholar   +1 more source

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