New completely regular q-ary codes based on Kronecker products

TL;DR

This paper introduces new infinite families of q-ary codes with specific regularity and packing properties, constructed explicitly using Kronecker products, expanding coding theory with novel code classes.

Contribution

It provides explicit constructions of completely regular and uniformly packed q-ary codes with arbitrary covering radius using Kronecker products, which was not previously established.

Findings

Constructed infinite families of completely regular codes with d=3

Derived intersection arrays for the codes

Presented uniformly packed codes that are not completely regular

Abstract

For any integer $\rho \geq 1$ and for any prime power q, the explicit construction of a infinite family of completely regular (and completely transitive) q-ary codes with d=3 and with covering radius $\rho$ is given. The intersection array is also computed. Under the same conditions, the explicit construction of an infinite family of q-ary uniformly packed codes (in the wide sense) with covering radius $\rho$, which are not completely regular, is also given. In both constructions the Kronecker product is the basic tool that has been used.