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

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International Journal of Informatics and Applied Mathematics
Volume:6 Issue:2
A Class of LCD Codes Through Cyclic Codes Over $ZpR$

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

Authors : Zineb Hebbache, Amit Sharma

Pages : 8-19

Doi:10.53508/ijiam.1213801

View : 40 | Download : 23

Publication Date : 2024-01-29

Article Type : Research Paper

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.
Keywords : Codes over mixed alphabets

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