# A concatenation construction for propelinear perfect codes from regular subgroups of GA(r,2)

## TL;DR

This paper introduces a new method to construct propelinear perfect binary codes of various lengths using a specific concatenation technique and regular subgroups of the affine group over GF(2).

## Contribution

It presents a novel concatenation construction for propelinear perfect codes based on regular subgroups of the affine group, extending code lengths beyond previous limits.

## Key findings

- Constructed new propelinear perfect codes for lengths greater than 7.
- Demonstrated the use of regular subgroups of GA(r,2) in code construction.
- Extended the known range of propelinear perfect codes.

## Abstract

A code $C$ is called propelinear if there is a subgroup of $Aut(C)$ of order $|C|$ acting transitively on the codewords of $C$. In the paper new propelinear perfect binary codes of any admissible length more than $7$ are obtained by a particular case of the Solov'eva concatenation construction--1981 and the regular subgroups of the general affine group of the vector space over $GF(2)$.