A Class of LCD Codes Through Cyclic Codes Over $ZpR$

Abstract

In recent time, some mixed types of alphabets have been considered for constructing error correcting codes. These constructions include $\bbbz_{2}\bbbz_{4}-$additive codes, $\bbbz_{2}\bbbz_{2}[u]-$linear codes et cetera. In this paper, we studied a class of codes over a mixed ring $\bbbz_{p}R$ where $R=\bbbz_{p}+v\bbbz_{p}+v^{2}\bbbz_{p}, v^{3}=v.$ We determined an algebraic structure of these codes under certain conditions. We have also constructed a class of LCD cyclic codes over $\bbbz_{p}R$. A necessary and sufficient condition for a cyclic code to be a complementary dual (LCD) code has been obtained.