Repeated-root bidimensional (&lt;i&gt;μ&lt;/i&gt;, &lt;i&gt;ν&lt;/i&gt;)-constacyclic codes of length 4&lt;i&gt;p&lt;/i&gt;&lt;SUP align="right"&gt;&lt;i&gt;t&lt;/i&gt;&lt;/SUP&gt;.2&lt;SUP align="right"&gt;&lt;i&gt;r&lt;/i&gt;&lt;/SUP&gt;

Patel, Shikha; Prakash, Om

doi:10.1504/ijicot.2020.110738

Cited by 1 publication

(1 citation statement)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The two-dimensional theory has many applications in the analysis and generation of twodimensional periodic arrays that help us to construct the two-dimensional feedback shift register with a minimum number of storage devices. Therefore, the study of these codes over finite rings has got the attention of many researchers and hence many new techniques have been discovered to produce cyclic codes over the finite commutative rings with better parameters, we refer [7,10,11,14,15].…”

Section: Introductionmentioning

confidence: 99%

A note on two-dimensional cyclic and constacyclic codes

Prakash,

Patel

2022

J. Algebra Comb. Discrete Appl.

View full text Add to dashboard Cite

During the study of the two-dimensional cyclic (TDC) codes of length $n=ls$ over a finite field $\mathbb{F}_q$ where $s=2^k$, Sepasdar and Khashyarmanesh (2016, [11]) arose a problem that the technique used by them to characterize TDC codes of length $n=ls$ does not work for TDC codes of length $3l$. It naturally motivates us to study the TDC codes of other lengths together with $3l$. Further, $(\lambda_1,\lambda_2)$-constacyclic codes are the generalization of constacyclic codes. Thus, we study two-dimensional cyclic codes of length $3l$ and $(\lambda_1,\lambda_2)$-constacyclic codes of length $2l$, respectively over finite fields. Here, the generating set of polynomials for these two-dimensional codes and their duals are obtained. Finally, with the help of our derived results, we have constructed many MDS codes corresponding to the two-dimensional codes.

show abstract

Section: Introductionmentioning

confidence: 99%