Skew Generalized Quasi-Cyclic Codes over Finite Fields

Gao, Jian; Shen, Linzhi; Fu, Fang-Wei

doi:10.48550/arxiv.1309.1621

Cited by 5 publications

(4 citation statements)

References 18 publications

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“…We close this section by mentioning idempotent generators of skew-constacyclic codes. In [16] the authors consider central moduli of the form x n −1. Such polynomials have a factorization into pairwise coprime two-sided maximal polynomials [22, Thm.…”

Section: Skew-constacyclic Codes and Their Dualsmentioning

confidence: 99%

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Skew-Polynomial Rings and Skew-Cyclic Codes

Gluesing-Luerssen

2019

Preprint

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This is a survey on the theory of skew-cyclic codes based on skew-polynomial rings of automorphism type. Skew-polynomial rings have been introduced and discussed by Ore (1933). Evaluation of skew polynomials and sets of (right) roots were first considered by Lam (1986) and studied in great detail by Lam and Leroy thereafter. After a detailed presentation of the most relevant properties of skew polynomials, we survey the algebraic theory of skew-cyclic codes as introduced by Boucher and Ulmer ( 2007) and studied by many authors thereafter. A crucial role will be played by skew-circulant matrices. Finally, skewcyclic codes with designed minimum distance are discussed, and we report on two different kinds of skew-BCH codes, which were designed in 2014 and later. * This survey will appear as a chapter in "A Concise Encyclopedia of Coding Theory" to be published by CRC Press.

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Section: Skew-constacyclic Codes and Their Dualsmentioning

confidence: 99%

“…Such polynomials have a factorization into pairwise coprime two-sided maximal polynomials [22, Thm. 1.2.17'], which in turn gives rise to a decomposition of F[x; σ]/(x n − 1) into a direct product of rings generated by central idempotents [16,Thm. 2.11].…”

Section: Skew-constacyclic Codes and Their Dualsmentioning

confidence: 99%

Skew-Polynomial Rings and Skew-Cyclic Codes

Gluesing-Luerssen

2019

Preprint

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“…In [1], T. Abualrub and P. Seneviratne studied skew cyclic codes over ring F 2 + vF 2 with v 2 = v. Moreover, J. Gao [6] and F. Gursoy et al [8] presented skew cyclic codes over F p + vF p and F q + vF q with different automorphisms, respectively. In [7], J. Gao et al also studied skew generalized quasi-cyclic codes over finite fields.…”

Section: Introductionmentioning

confidence: 99%

Skew Cyclic codes over $\F_q+u\F_q+v\F_q+uv\F_q$

Yao¹,

Shi²,

Solé³

2015

Preprint

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“…Many methods and many approaches are applied to produce certain types of codes with good parameters and properties. Some authors generalized the notion of cyclic, quasi-cyclic and constacyclic codes by using generator polynomials in skew polynomial rings [7,8,9,10,12,15,16,18,21,24,29,30].…”

Section: Introductionmentioning

confidence: 99%

On the codes over the Z_3+vZ_3+v^2Z_3

Dertli,

Cengellenmis,

Eren

2015

Preprint

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In this paper, we study the structure of cyclic, quasi-cyclic, constacyclic codes and their skew codes over the finite ring R = Z3 +vZ3 +v 2 Z3, v 3 = v. The Gray images of cyclic, quasi-cyclic, skew cyclic, skew quasicyclic and skew constacyclic codes over R are obtained. A necessary and sufficient condition for cyclic (negacyclic) codes over R that contains its dual has been given. The parameters of quantum error correcting codes are obtained from both cyclic and negacyclic codes over R. It is given some examples. Firstly, quasi-constacyclic and skew quasi-constacyclic codes are introduced. By giving two Hermitian product, it is investigated their duality. A sufficient condition for 1-generator skew quasiconstacyclic codes to be free is determined.

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Skew Generalized Quasi-Cyclic Codes over Finite Fields

Cited by 5 publications

References 18 publications

Skew-Polynomial Rings and Skew-Cyclic Codes

Skew-Polynomial Rings and Skew-Cyclic Codes

Skew Cyclic codes over $\F_q+u\F_q+v\F_q+uv\F_q$

On the codes over the Z_3+vZ_3+v^2Z_3

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