# Rank weights for arbitrary finite field extensions

## TL;DR

This paper investigates various definitions of generalized rank weights for arbitrary finite field extensions, proving their equivalence and extending known results from finite fields to more general cases.

## Contribution

It introduces and proves the equivalence of multiple definitions of generalized rank weights for arbitrary finite field extensions, broadening the scope of previous finite field results.

## Key findings

- All definitions of generalized rank weights coincide for arbitrary finite extensions.
- The results generalize known finite field extension theorems.
- Provides a unified framework for rank weights in general finite field extensions.

## Abstract

In this paper, we study several definitions of generalized rank weights for arbitrary finite extensions of fields. We prove that all these definitions coincide, generalizing known results for extensions of finite fields.