Goppa codes over Edwards curves

TL;DR

This paper develops a method to construct algebraic-geometric Goppa codes from Edwards curves by explicitly determining a basis for the Riemann-Roch space of certain divisors, enabling code generation.

Contribution

It introduces a way to compute bases for Riemann-Roch spaces on Edwards curves, facilitating the construction of Goppa codes from these curves.

Findings

Explicit basis for Riemann-Roch space on Edwards curves

Method to compute generating matrices for Goppa codes

Extension of algebraic-geometric coding techniques to Edwards curves

Abstract

Given an Edwards curve, we determine a basis for the Riemann-Roch space of any divisor whose support does not contain any of the two singular points. This basis allows us to compute a generating matrix for an algebraic-geometric Goppa code over the Edwards curve.