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

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 2n × 2n Hadamard MDS matrices in the finite field GF(2q). In addition to introducing this method, we present a direct method for the inversion of a special class of 2n × 2n Vandermonde matrices.

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Correspondence to Mahdi Sajadieh.

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Communicated by J. Jedwab.

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Sajadieh, M., Dakhilalian, M., Mala, H. et al. On construction of involutory MDS matrices from Vandermonde Matrices in GF(2q). Des. Codes Cryptogr. 64, 287–308 (2012). https://doi.org/10.1007/s10623-011-9578-x

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Keywords

  • MDS matrix
  • Vandermonde matrix
  • Hadamard matrix
  • Blockcipher

Mathematics Subject Classification (2000)

  • 11T71
  • 14G50
  • 51E22
  • 94B05
  • 20H30
  • 15A09