# The complexity of MinRank

## TL;DR

This paper provides a concise, rigorous proof of the complexity of the generalized MinRank problem, extending previous results and covering both under-defined and well-defined cases.

## Contribution

It offers a new, simplified proof for the MinRank problem's complexity, building upon and extending prior work by Faugère et al.

## Key findings

- Extended the complexity analysis to both under-defined and well-defined cases
- Provided a rigorous proof that clarifies previous results
- Unified previous partial results into a comprehensive framework

## Abstract

In this note, we leverage some of our results from arXiv:1706.06319 to produce a concise and rigorous proof for the complexity of the generalized MinRank Problem in the under-defined and well-defined case. Our main theorem recovers and extends previous results by Faug\`ere, Safey El Din, Spaenlehauer (arXiv:1112.4411).