# Completely regular codes by concatenating Hamming codes

## TL;DR

This paper introduces new families of completely regular codes created through concatenation of cyclic Hamming codes, analyzing their intersection arrays and conditions for complete regularity and transitivity.

## Contribution

It presents novel constructions of completely regular codes using concatenation of Hamming codes and studies their properties and extensions.

## Key findings

- Constructed new families of completely regular codes
- Computed intersection arrays for these codes
- Identified conditions for code extensions to remain completely regular

## Abstract

We construct new families of completely regular codes by concatenation methods. By combining parity check matrices of cyclic Hamming codes, we obtain families of completely regular codes. In all cases, we compute the intersection array of these codes. We also study when the extension of these codes gives completely regular codes. Some of these new codes are completely transitive.