# AGC, t-designs and partition sets

## TL;DR

This paper explores the geometric representation of AG codes within Grassmannians and demonstrates that certain invariant subgrassmannians form t-designs with specific parameters, advancing the understanding of algebraic geometry codes.

## Contribution

It establishes that invariant subgrassmannians under triangle group actions are t-designs, providing new insights into the geometric structure of AG codes.

## Key findings

- Invariant subgrassmannians form t-designs with specific parameters
- Triangle group actions preserve certain geometric structures
- Enhanced understanding of AG code geometry

## Abstract

AG codes correspond geometrically to points in the Grassmannian of k-planes in an n-dimensional projective space PG(n, F_q) defined over a finite field F_q of q elements. We prove that invariant subgrassmannians by the action of a triangle group hold a t-design of determined parameters.