Designs, Codes and Cryptography

, Volume 87, Issue 2–3, pp 249–260 | Cite as

On circulant involutory MDS matrices

  • Victor Cauchois
  • Pierre LoidreauEmail author
Part of the following topical collections:
  1. Special Issue: Coding and Cryptography


We give a new algebraic proof of the non-existence of circulant involutory MDS matrices with coefficients in fields of characteristic 2. In odd characteristics we give parameters for the potential existence. If we relax circulancy to \(\theta \)-circulancy, then there is no restriction to the existence of \(\theta \)-circulant involutory MDS matrices even for fields of characteristic 2. Finally, we relax further the involutory definition and propose a new direct construction of almost involutory \(\theta \)-circulant MDS matrices. We show that they can be interesting in hardware implementations.


MDS codes Involutory matrices Diffusion layers Gabidulin codes 

Mathematics Subject Classification

94B05 68R99 94A60 



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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.DGA MIRennes Cedex 9France
  2. 2.Univ Rennes, CNRS, IRMAR - UMR 6625RennesFrance

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