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Designs, Codes and Cryptography

, Volume 64, Issue 3, pp 287–308 | Cite as

On construction of involutory MDS matrices from Vandermonde Matrices in GF(2 q )

  • Mahdi Sajadieh
  • Mohammad Dakhilalian
  • Hamid Mala
  • Behnaz Omoomi
Article

Abstract

Due to their remarkable application in many branches of applied mathematics such as combinatorics, coding theory, and cryptography, Vandermonde matrices have received a great amount of attention. Maximum distance separable (MDS) codes introduce MDS matrices which not only have applications in coding theory but also are of great importance in the design of block ciphers. Lacan and Fimes introduce a method for the construction of an MDS matrix from two Vandermonde matrices in the finite field. In this paper, we first suggest a method that makes an involutory MDS matrix from the Vandermonde matrices. Then we propose another method for the construction of 2 n × 2 n Hadamard MDS matrices in the finite field GF(2 q ). In addition to introducing this method, we present a direct method for the inversion of a special class of 2 n  × 2 n Vandermonde matrices.

Keywords

MDS matrix Vandermonde matrix Hadamard matrix Blockcipher 

Mathematics Subject Classification (2000)

11T71 14G50 51E22 94B05 20H30 15A09 

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Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  • Mahdi Sajadieh
    • 1
  • Mohammad Dakhilalian
    • 1
  • Hamid Mala
    • 2
  • Behnaz Omoomi
    • 3
  1. 1.Cryptography & System Security Research Laboratory, Department of Electrical and Computer EngineeringIsfahan University of TechnologyIsfahanIran
  2. 2.Department of Information Technology EngineeringUniversity of IsfahanIsfahanIran
  3. 3.Department of Mathematical SciencesIsfahan University of TechnologyIsfahanIran

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