F&lt;SUB align="right"&gt;3R-skew cyclic codes

Sharma, Amit K.; Bhaintwal, Maheshanand

doi:10.1504/ijicot.2016.076967

Cited by 4 publications

(2 citation statements)

References 7 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Further, we extend the study to skew constacyclic codes in the sense of [17]. While skew cyclic codes have been studied extensively since that reference (see publications 1,4,5,6,8,9,10 in [35]), it is only the fourth time that they occur in a mixed alphabet setting [11,12,28]. The present article shows some algebraic richness of skew codes over the mentioned mixed alphabets.…”

Section: Introductionmentioning

confidence: 62%

$ \mathbb{Z}_{4}\mathbb{Z}_{4}[u] $-additive cyclic and constacyclic codes

Islam¹,

Prakash²,

Solé³

2021

AMC

View full text Add to dashboard Cite

We study mixed alphabet cyclic and constacyclic codes over the two alphabets Z 4 , the ring of integers modulo 4, and its quadratic extension Z 4 [u] = Z 4 + uZ 4 , u 2 = 0. Their generator polynomials and minimal spanning sets are obtained. Further, under new Gray maps, we find cyclic, quasi-cyclic codes over Z 4 as the Gray images of both λ-constacyclic and skew λ-constacyclic codes over Z 4 [u]. Moreover, it is proved that the Gray images of Z 4 Z 4 [u]-additive constacyclic and skew Z 4 Z 4 [u]-additive constacyclic codes are generalized quasi-cyclic codes over Z 4 . Finally, several new quaternary linear codes are obtained from these cyclic and constacyclic codes.

show abstract

Section: Introductionmentioning

confidence: 62%

$ \mathbb{Z}_{4}\mathbb{Z}_{4}[u] $-additive cyclic and constacyclic codes

Islam¹,

Prakash²,

Solé³

2021

AMC

View full text Add to dashboard Cite

show abstract

“…This work was then extended to arbitrary length in [26]. Further, work has been done on codes over rings that are extensions of finite fields such as F 2 + vF 2 in [1], F 3 + vF 3 in [2], F p + vF p in [13], [16] and also over mixed alphabets like F 3 (F 3 + uF 3 ) in [24], [7] .…”

mentioning

confidence: 99%

A complete structure of skew cyclic codes over $ \mathbb{Z}_4+u\mathbb{Z}_4 $

Shah,

Sharma

2025

AMC

Self Cite

View full text Add to dashboard Cite

In this paper, we study a class of skew cyclic codes over the ring R = Z 4 + uZ 4 , with u 2 = 1. We determine a complete structure of skew cyclic codes over R by investigating the generating sets of these codes. Additionally, we have identified some more conditions on generating polynomials for these codes when dealing with odd lengths, and in this case, the skew-cyclic codes are equivalent to cyclic codes. Some examples have been given to illustrate the results. Moreover, we present some examples of skew cyclic codes over R whose Z 4 images give some new linear codes over Z 4 .

show abstract

A class of 2D skew-cyclic codes over $${\mathbb {F}}_{q}+u{\mathbb {F}}_{q}$$

Sharma

Bhaintwal

2019

AAECC

View full text Add to dashboard Cite

F<SUB align="right">3R-skew cyclic codes

Cited by 4 publications

References 7 publications

$ \mathbb{Z}_{4}\mathbb{Z}_{4}[u] $-additive cyclic and constacyclic codes

$ \mathbb{Z}_{4}\mathbb{Z}_{4}[u] $-additive cyclic and constacyclic codes

A complete structure of skew cyclic codes over $ \mathbb{Z}_4+u\mathbb{Z}_4 $

A class of 2D skew-cyclic codes over $${\mathbb {F}}_{q}+u{\mathbb {F}}_{q}$$

Contact Info

Product

Resources

About