MDS matrices and involutive MDS matrices are widely used in block ciphers. This paper will examine those MDS matrices that are both Hadamard matrices and Cauchy matrices, and give the structure, construction method and number of such matrices, thereby obtaining a new construction method for MDS matrices. This paper also proves that Cauchy-Hadamard type MDS matrices are equivalent to involutive Cauchy-Hadamard type MDS matrices, and gives a method to construct involutive Cauchy-Hadamard type MDS matrices from Cauchy-Hadamard type MDS matrices.
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