# Non-linear maximum rank distance codes in the cyclic model for the field reduction of finite geometries

## TL;DR

This paper constructs infinite families of non-linear maximum rank distance codes using bilinear forms and finite geometry models, extending recent results and providing a geometric perspective on these codes.

## Contribution

It introduces new infinite families of non-linear maximum rank distance codes via geometric methods and relates them to existing codes in the literature.

## Key findings

- Constructed infinite families of non-linear maximum rank distance codes.
- Provided a geometric description using the cyclic model for field reduction.
- Unified and extended previous non-linear code constructions.

## Abstract

In this paper we construct infinite families of non-linear maximum rank distance codes by using the setting of bilinear forms of a finite vector space. We also give a geometric description of such codes by using the cyclic model for the field reduction of finite geometries and we show that these families contain the non-linear maximum rank distance codes recently provided by Cossidente, Marino and Pavese.