On the $Z_q$-MacDonald Code and its Weight Distribution of dimension 3

TL;DR

This paper determines the parameters and weight distribution of $\

Contribution

It provides the first explicit weight distribution for $\

Findings

Parameters of $\

Weight distribution of $\

Results valid for all $q \\geq 2$

Abstract

In this paper, we determine the parameters of $\mathbb{Z}_q$-MacDonald Code of dimension k for any positive integer $q \geq 2.$ Further, we have obtained the weight distribution of $\mathbb{Z}_q$-MacDonald code of dimension 3 and furthermore, we have given the weight distribution of $\mathbb{Z}_q$-Simplex code of dimension 3 for any positive integer $q \geq 2.$