# Relative Generalized Minimum Distance Functions

## TL;DR

This paper introduces the relative generalized minimum distance function (RGMDF) and the relative generalized footprint function, providing algebraic tools to analyze and bound the relative generalized Hamming weights of projective Reed--Muller--type codes.

## Contribution

The paper presents the RGMDF and the relative generalized footprint function, offering new algebraic methods and bounds for analyzing projective Reed--Muller--type codes.

## Key findings

- RGMDF provides an algebraic approach to relative generalized Hamming weights.
- The relative generalized footprint function offers a tight, easily computable lower bound for RGMDF.
- The methods improve understanding of code weight distributions.

## Abstract

In this paper we introduce the relative generalized minimum distance function (RGMDF for short) and it allows us to give an algebraic approach to the relative generalized Hamming weights of the projective Reed--Muller--type codes. Also we introduce the relative generalized footprint function and it gives a tight lower bound for the RGMDF which is much easier to compute.