On the existence of involutory circulant MDS matrices over fields with odd characteristic
Abstract
In 2019, Cauchois and Loidreau derived key conditions for the existence of maximum distance separable (MDS), involutory, and circulant matrices over field Fq with odd characteristic p. They conjectured that the necessary conditions are also sufficient. In this article, we disprove this conjecture by giving two counterexamples. One counterexample is based on a theorem of Adhiguna et al., and another one is based on a modification of a theorem of Cauchois and Loidreau on the necessary conditions above. Finally, we give examples showing that the non-trivial involutory circulant MDS matrix over Fq exists for all odd prime powers q = pr, where p > 3.
Fields of Study & Subjects
Coding theory and cryptography
Cryptographic Implementations and Security
Matrix Theory and Algorithms
Publication details
- Journal / source
- AIP conference proceedings
- Volume
- 3326
- Pages
- 030005–030005
- Publication date
- 1 January 2026
- Language
- EN