The permutation group of Reed-Solomon codes over arbitrary points

TL;DR

This paper characterizes the permutation group of Reed-Solomon codes over arbitrary points, showing it consists of degree-one polynomials that preserve the evaluation set, thus generalizing known cases.

Contribution

It provides a unified proof describing the permutation group of Reed-Solomon codes for arbitrary evaluation points, extending previous results.

Findings

Permutation group characterized by degree-one polynomials

Results apply to arbitrary evaluation point sets

Simplifies understanding of Reed-Solomon code symmetries

Abstract

In this work, we prove that the permutation group of a Reed-Solomon code is given by the polynomials of degree one that leave the set of evaluation points invariant. Our results provide a straightforward proof of the well-known cases of the permutation group of the Reed-Solomon code when the set of evaluation points is the whole finite field or the multiplicative group.