Hommogenous weights on the ring $\mathfrak{R}_{5,3}=\mathbb{F}_5+u_1\mathbb{F}_5+u_2\mathbb{F}_5+u_3\mathbb{F}_5$

Abstract

In this paper, we investigate linear codes over the ring $ \mathfrak{R}_{5,3}=\mathbb{F}_{5}+u_{1}\mathbb{F}_{5}+u_{2}\mathbb{F}_{5}+u_{3}\mathbb{F}_{5} $, and we determine the homogeneous weight of this ring, to derive some properties corresponding to these codes.