Bases for Riemann-Roch spaces of one point divisors on an optimal tower of function fields

TL;DR

This paper presents an algorithm for explicitly computing bases of Riemann-Roch spaces of one point divisors on an optimal tower of function fields, aiding algebraic geometric code applications.

Contribution

It introduces a new algorithm for computing bases and Weierstrass semigroups on an optimal tower of function fields, including explicit computations up to level eight.

Findings

Algorithm successfully computes bases for one point divisors

Explicit Weierstrass semigroups are obtained up to level eight

Enhances understanding of function field structures for coding theory

Abstract

For applications in algebraic geometric codes, an explicit description of bases of Riemann-Roch spaces of divisors on function fields over finite fields is needed. We give an algorithm to compute such bases for one point divisors, and Weierstrass semigroups over an optimal tower of function fields. We also explicitly compute Weierstrass semigroups till level eight.