Grassl–Rötteler cyclic and consta-cyclic MDS codes are generalised Reed–Solomon codes

Abstract

We prove that the cyclic and constacyclic codes constructed by Grassl and Rötteler in International Symposium on Information Theory (ISIT), pp. 1104–1108 (2015) are generalised Reed–Solomon codes. This note can be considered as an addendum to Grassl and Rötteler International Symposium on Information Theory (ISIT), pp 1104–1108 (2015). It can also be considered as an appendix to Ball and Vilar IEEE Trans Inform Theory 68:3796–3805, (2022) where Conjecture 11 of International Symposium on Information Theory (ISIT), pp 1104–1108 (2015), which was stated for Grassl–Rötteler codes, is proven for generalised Reed–Solomon codes. The content of this note, together with IEEE Trans Inform Theory 68:3796–3805, (2022) therefore implies that Conjecture 11 from International Symposium on Information Theory (ISIT), pp. 1104–1108 (2015) is true.