A Graph Aided Strategy to Produce Good Recursive Towers over Finite Fields

TL;DR

This paper introduces a systematic graph-based method for constructing recursive towers over finite fields, combining computational tools and theoretical criteria to ensure many rational points and analyze tower parameters.

Contribution

It presents a novel graph-aided approach and theoretical functional criteria for producing and studying potentially good recursive towers over finite fields.

Findings

Successful example demonstrating the method

Theoretical criterion for rational points existence

Analysis of tower parameters using the criterion

Abstract

We propose a systematic method to produce potentially good recursive towers over finite fields. The graph point of view, so as some magma and sage computations are used in this process. We also establish some theoretical functional criterion ensuring the existence of many rational points on a recursive tower. Both points are illustrated on an example, from the production process, to the theoretical study, using this functional criterion, of the parameters of the obtained potentially good tower.