Good recursive towers over prime fields exist

TL;DR

This paper presents a construction and explicit equations for good recursive towers over finite fields with prime power order, excluding fields with q=2 or 3, advancing the understanding of algebraic geometry codes.

Contribution

It introduces a new method to construct good recursive towers over prime fields, providing explicit equations for these towers.

Findings

Constructed recursive towers over finite fields with q ≠ 2,3

Provided explicit equations for these towers

Demonstrated the towers are 'good' in coding theory terms

Abstract

We give a construction and equations for good recursive towers over any finite field $\mathbf{F}_q$ with $q \ne 2$ and $3$.