The Grassl-R\"otteler cyclic and consta-cyclic MDS codes are generalised Reed-Solomon codes

TL;DR

This paper proves that certain cyclic and constacyclic codes are actually generalized Reed-Solomon codes, confirming a conjecture and extending previous results in coding theory.

Contribution

It demonstrates that Grassl-Rötteler cyclic and constacyclic codes are generalized Reed-Solomon codes, confirming a conjecture and providing an important link between these code classes.

Findings

Grassl-Rötteler codes are GRS codes

Conjecture 11 from arXiv:1502.0526 is proven true

Extension of previous results on code classification

Abstract

We prove that the cyclic and constacyclic codes constructed by Grassl and R\"otteler in arXiv:1502.05267 are generalised Reed-Solomon codes. This note can be considered as an addendum to that article. It can also be considered as an appendix to arXiv:2106.10180, where Conjecture 11 of arXiv:1502.0526, which was stated for Grassl-R\"otteler codes, is proven for generalised Reed-Solomon codes. The content of this note, together with arXiv:2106.10180, therefore implies that Conjecture 11 from arXiv:1502.0526 is true.