Paper Info
Title
Complete classification for simple root cyclic codes over local rings $\mathbb{Z}_{p^s}[v]/\langle v^2-pv\rangle$.
Abstract
Let $p$ be a prime integer, $n,sgeq 2$ be integers satisfying ${rm gcd}(p,n)=1$, and denote $R=mathbb{Z}_{p^s}[v]/langle v^2-pvrangle$. Then $R$ is a local non-principal ideal ring of $p^{2s}$ elements. First, the structure of any cyclic code over $R$ of length $n$ and a complete classification of all these codes are presented. Then the cardinality of each code and dual codes of these codes are given. Moreover, self-dual cyclic codes over $R$ of length $n$ are investigated. Finally, we list some optimal $2$-quasi-cyclic self-dual linear codes over $mathbb{Z}_4$ of length $30$ and extremal $4$-quasi-cyclic self-dual binary linear $[60,30,12]$ codes derived from cyclic codes over $mathbb{Z}_{4}[v]/langle v^2+2vrangle$ of length $15$.
Year
Venue
Field
2017
arXiv: Information Theory
Prime (order theory),Integer,Discrete mathematics,Ideal (ring theory),Local ring,Cyclic code,Cardinality,Mathematics,Binary number
DocType
Volume
Citations 
Journal
abs/1710.09236
0
PageRank 
References 
Authors
0.34
0
2
Name
Order
Citations
PageRank
Yuan Cao154835.60
Yonglin Cao24615.88