# Evaluation codes and their basic parameters

## TL;DR

This paper provides formulas and bounds for generalized Hamming weights of evaluation codes, including Reed--Muller, toric, and squarefree codes, advancing understanding of their parameters and minimum distances.

## Contribution

It introduces degree formulas for generalized Hamming weights and establishes lower bounds, specifically analyzing Reed--Muller, toric, and squarefree evaluation codes.

## Key findings

- Degree formulas for generalized Hamming weights of Reed--Muller codes
- Minimum distance of toric codes over hypersimplices determined
- First and second generalized Hamming weights of squarefree evaluation codes identified

## Abstract

The aim of this work is to give degree formulas for the generalized Hamming weights of evaluation codes and to show lower bounds for these weights. In particular, we give degree formulas for the generalized Hamming weights of Reed--Muller-type codes, and we determine the minimum distance of toric codes over hypersimplices, and the 1st and 2nd generalized Hamming weights of squarefree evaluation codes.