On Various Parameters of $Z_q$-Simplex codes for an even integer q

TL;DR

This paper investigates the parameters of $Z_q$-Simplex codes for even integers q, including their construction, parameters, and bounds on covering radius, contributing to the understanding of these algebraic codes.

Contribution

It introduces the construction of $Z_q$-Simplex and $Z_q$-MacDonald codes and establishes bounds on their covering radius for even q.

Findings

Constructed $Z_q$-Simplex and $Z_q$-MacDonald codes.

Derived parameters for these codes.

Provided bounds on the covering radius for even q.

Abstract

In this paper, we defined the $Z_q$-linear codes and discussed its various parameters. We constructed $Z_q$-Simplex code and $Z_q$-MacDonald code and found its parameters. We have given a lower and an upper bounds of its covering radius for q is an even integer.