1-Generator quasi-cyclic and generalized quasi-cyclic codes over the ring 
                $$\frac{{{\mathbb {Z}_4}[u]}}{{\left\langle {{u^2} - 1}\right\rangle }}$$
                
                    
                                    
                        
                            
                                
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Gao, Yun; Gao, Jian; Wu, Tingting; Fu, Fang-Wei

doi:10.1007/s00200-017-0315-1

Cited by 8 publications

(2 citation statements)

References 11 publications

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“…Xu [10] studied the quasi-twisted codes over ring Z 4 and obtained a new class of codes. J. Gao [11]studied minimal generation sets of three types of one-generator quasi-twisted codes over F 2 + uF 2 , which brought new ideas for the study of linear codes over finite commutative rings. For example, H. Q. Dinh [12] investigated the algebraic structure of λ-constacyclic codes over finite commutative semi-simple rings and obtained the necessary and sufficient conditions for the existence of self-dual, LCD, and Hermitian dual containing λ-constacyclic codes over finite commutative semi-simple rings.…”

Section: Introductionmentioning

confidence: 99%

Quasi~λ-cyclic Codes Over a Class of Finite Commutative Semi-simple Rings

Wang

Heng

et al. 2023

Preprint

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In coding theory, quasi λ-cyclic codes form an important class of codes which have been extensively studied. In this paper, we investigate the algebraic structure of quasi λ-cyclic codes over finite commutative semi simple rings. And we establish the relationship between quasi λ-cyclic codes over finite commutative semi-simple ring R and quasi λ-cyclic codes over finite fields Fq. Furthermore, we decompose quasi λ-cyclic codes to a direct sum of component codes C linear codes over rings, give the decomposition of quasi λ-cyclic codes and describe its dual codes.

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Section: Introductionmentioning

confidence: 99%

Quasi~λ-cyclic Codes Over a Class of Finite Commutative Semi-simple Rings

Wang

Heng

et al. 2023

Preprint

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“…Further, when a quasi-cyclic code is generated by a single element as a module over some auxiliary ring, then it is called a 1-generator quasi-cyclic code. Such codes have been studied in several series of papers [4,6,7,25,27,33]. Here, we obtain the algebraic structure of 1-generator quasi-cyclic codes over R 3 by using their generators and minimal spanning sets.…”

Section: Introductionmentioning

confidence: 99%

Self-dual and LCD double circulant codes over a class of non-local rings

et al. 2022

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Let F q be a finite field of order q = p m where p is an odd prime. This paper presents the study of self-dual and LCD double circulant codes over a class of finite commutative non-chain rings R q = F q +uF q +u 2 F q +• • •+u q−1 F q where u q = u. Here, the whole contribution is two-folded. Firstly, we enumerate self-dual and LCD double circulant codes of length 2n over R q , where n is an odd integer. Then by considering a dual-preserving Gray map ϕ, we show that Gray images of such codes are asymptotically good. Secondly, we investigate the algebraic structure of 1-generator quasi-cyclic (QC) codes over R q for q = 3. In that context, we present their generator polynomials along with their minimal generating sets and minimum distance bounds. Here, it is proved that ϕ(C) is an sq-QC code of length nq over F q if C is an s-QC code of length n over R q .

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On quasi-twisted codes and generalized quasi-twisted codes over $$\mathbb {Z}_{4} +u\mathbb {Z}_{4}$$

Mounir,

Haily

2024

Cryptogr. Commun.

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1-Generator quasi-cyclic and generalized quasi-cyclic codes over the ring $$\frac{{{\mathbb {Z}_4}[u]}}{{\left\langle {{u^2} - 1}\right\rangle }}$$ Z 4 [

Cited by 8 publications

References 11 publications

Quasi~λ-cyclic Codes Over a Class of Finite Commutative Semi-simple Rings

Quasi~λ-cyclic Codes Over a Class of Finite Commutative Semi-simple Rings

Self-dual and LCD double circulant codes over a class of non-local rings

On quasi-twisted codes and generalized quasi-twisted codes over $$\mathbb {Z}_{4} +u\mathbb {Z}_{4}$$

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