Constacyclic and Negacyclic Codes over $\mathbb{F}_{2}+u\mathbb{F}_{2}+v\mathbb{F}_{2}$ and their Equivalents over $\mathbb{F}_{2}$

Abstract

In this work, we consider the finite ring F_2 +uF_2 +vF_2, u^2 = 1;v^2 = 0, u.v = v.u = 0 which is not Frobenius and chain ring. We studied constacyclic and negacyclic codes over F_2+uF_2+vF_2 of odd length. These codes are compared with codes that had priorly been obtained on the finite field F_2. Moreover, we indicate that the Gray image of a constacyclic and negacyclic code over F_2+uF_2+vF_2 of odd length n is a quasicyclic code of index 4 with length 4n over F_2. In particular, the Gray images are applied to two different rings S_1 = F_2+vF_2, v^2 = 0 and S_2 = F_2+uF_2, u^2 = 1 and negacyclic and constacyclic images of these rings are also discussed.