Codes over an infinite family of rings with a Gray map

Çengellenmiş, Yasemin; Dertli, Abdullah; Dougherty, Steven T.

doi:10.1007/s10623-012-9787-y

Cited by 38 publications

(44 citation statements)

References 9 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…3, by using Gray map (see Ref. 9), we show that if C is self orthogonal so is ÉðCÞ: In Sec. 4, a su±cient and necessary condition for cyclic code over A 2 that contains its dual is given.…”

Section: Introductionmentioning

confidence: 92%

On quantum codes obtained from cyclic codes over A₂

Dertli

Çengellenmiş

Eren

2015

Int. J. Quantum Inform.

Self Cite

View full text Add to dashboard Cite

In this paper, quantum codes from cyclic codes over A 2 ¼ F 2 þ uF 2 þ vF 2 þ uvF 2 ; u 2 ¼ u; v 2 ¼ v; uv ¼ vu, for arbitrary length n have been constructed. It is shown that if C is self orthogonal over A 2 ; then so is ÉðCÞ, where É is a Gray map. A necessary and su±cient condition for cyclic codes over A 2 that contains its dual has also been given. Finally, the parameters of quantum error correcting codes are obtained from cyclic codes over A 2 .

show abstract

Section: Introductionmentioning

confidence: 92%

On quantum codes obtained from cyclic codes over A₂

Dertli

Çengellenmiş

Eren

2015

Int. J. Quantum Inform.

Self Cite

View full text Add to dashboard Cite

show abstract

“…Codes over the ring F 2 + vF 2 have been studied in numerous papers, see [1,6,7] for example. This family of rings has been generalized to the family of rings A k in [4].…”

Section: Introductionmentioning

confidence: 99%

Θ_S-cyclic codes overA_k

Barra

Dougherty

Muchlis

et al. 2016

International Journal of Computer Mathematics: Computer Systems

View full text Add to dashboard Cite

show abstract

“…Since the revelation in 1994 [17], there has been a lot of interest in codes over finite rings. The structure of a certain type of codes over many rings are determined such as negacyclic, cyclic, quasi-cyclic, consta cyclic codes in [6,11,20,21,22,23,26,32]. Many methods and many approaches are applied to produce certain types of codes with good parameters and properties.…”

Section: Introductionmentioning

confidence: 99%

On the Codes over a Semilocal Finite Ring

Dertli¹,

Çengellenmiş²,

Eren³

2015

ijacsa

Self Cite

View full text Add to dashboard Cite

Abstract-In this paper, we study the structure of cyclic, quasi cyclic, constacyclic codes and their skew codes over the finite ring R. The Gray images of cyclic, quasi cyclic, skew cyclic, skew quasi cyclic 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. Some examples are given. Firstly, quasi constacyclic and skew quasi constacyclic codes are introduced. By giving two inner product, it is investigated their duality. A sufficient condition for 1 generator skew quasi constacyclic codes to be free is determined.

show abstract

Codes over an infinite family of rings with a Gray map

Cited by 38 publications

References 9 publications

On quantum codes obtained from cyclic codes over A₂

On quantum codes obtained from cyclic codes over A₂

Θ_S-cyclic codes overA_k

On the Codes over a Semilocal Finite Ring

Contact Info

Product

Resources

About

Codes over an infinite family of rings with a Gray map

Cited by 38 publications

References 9 publications

On quantum codes obtained from cyclic codes over A2

On quantum codes obtained from cyclic codes over A2

ΘS-cyclic codes overAk

On the Codes over a Semilocal Finite Ring

Contact Info

Product

Resources

About

On quantum codes obtained from cyclic codes over A₂

On quantum codes obtained from cyclic codes over A₂

Θ_S-cyclic codes overA_k