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

Emmanuel Hallouin (1) , Marc Perret (1)

1 IMT - Institut de Mathématiques de Toulouse UMR5219

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 by an example, from the production process, to the theoretical study.

Mots clés: Algebraic curves; Finite fields; Rational points

Domaines: Théorie des nombres [math.NT]; Géométrie algébrique [math.AG]

Emmanuel Hallouin, Marc Perret. A Graph Aided Strategy to Produce Good Recursive Towers over Finite Fields. Finite Fields and Their Applications, 2016, 42, pp.200-224. ⟨10.1016/j.ffa.2016.07.008⟩. ⟨hal-01136424⟩