Puncturing maximum rank distance codes

TL;DR

This paper studies punctured maximum rank distance codes in cyclic models, revealing many are not equivalent to known Gabidulin codes, and computes their automorphism groups.

Contribution

It introduces a new family of punctured MRD codes in cyclic models and proves many are inequivalent to existing Gabidulin codes, solving a recent open problem.

Findings

Identified a new family of MRD codes via puncturing generalized twisted Gabidulin codes.

Calculated the automorphism group of these punctured codes.

Proved many codes in this family are not equivalent to any generalized Gabidulin code.

Abstract

We investigate punctured maximum rank distance codes in cyclic models for bilinear forms of finite vector spaces. In each of these models we consider an infinite family of linear maximum rank distance codes obtained by puncturing generalized twisted Gabidulin codes. We calculate the automorphism group of such codes and we prove that this family contains many codes which are not equivalent to any generalized Gabidulin code. This solves a problem posed recently by Sheekey in [30].