q-ary Propelinear Perfect Codes from the Regular Subgroups of the GA(r,q) and Their Ranks

TL;DR

This paper introduces a novel method for constructing q-ary propelinear perfect codes using automorphisms of regular subgroups of the affine group, resulting in an infinite series of codes with varying ranks for prime q.

Contribution

It presents a new construction technique for q-ary propelinear perfect codes based on automorphisms of regular subgroups, expanding the known classes of such codes.

Findings

Constructed an infinite series of q-ary propelinear perfect codes

Codes have varying ranks and increasing length for prime q

Method leverages automorphisms of regular subgroups of the affine group

Abstract

We propose a new method of constructing q-ary propelinear perfect codes. The approach utilizes permutations of the fixed length q-ary vectors that arise from the automorphisms of the regular subgroups of the affine group. For any prime q it is shown that the new class contains an infinite series of q-ary propelinear perfect codes of varying ranks of growing length.