In this paper security aspects of the existing symmetric key encryption schemes based on Hadamard matrices are examined. Hadamard matrices itself have symmetries like one circulant core or two circulant core. Here, we are exploiting the inherent symmetries of Hadamard matrices and are able to perform attacks on these encryption schemes. It is found that entire key can be obtained by observing t...

Forty years ago, Goethals and Seidel showed that if the adjacency algebra of a strongly regular graph X contains a Hadamard matrix then X is of Latin square type or of negative Latin square type [8]. We extend their result to complex Hadamard matrices and find only three additional families of parameters for which the strongly regular graphs have complex Hadamard matrices in their adjacency alg...

AHadamard matrix is said to be completely non-cyclic (CNC) if there are no two rows (or two columns) that are shift equivalent in its reduced form. In this paper, we present three new constructions of CNC Hadamard matrices. We give a primary construction using a flipping operation on the submatrices of the reduced form of a Hadamard matrix. We show that, up to some restrictions, the Kronecker p...

In this paper we formalize three constructions for skew-Hadamard matrices from a Computational Algebra point of view. These constructions are the classical 4 Williamson array construction, an 8 Williamson array construction and a construction based on OD(16; 1, 1, 2, 2, 2, 2, 2, 2, 2), a 9-variable full orthogonal design of order 16. Using our Computational Algebra formalism in conjunction with...

Let H be a Hadamard matrix of order 24. In this note, we show that the extremality of the binary code of H is equivalent to the extremality of the ternary code of HT . This fact has been observed by Assmus and Key [1], as a result of the complete classification of Hadamard matrices of order 24. Our proof is a consequence of more general results on the minimum weight of the dual code of the code...

*Correspondence: [email protected]; [email protected]; [email protected] 1School of Mathematics and Computational Science, Xiangtan University, Xiangtan, Hunan 411105, P.R. China Full list of author information is available at the end of the article Abstract In this paper, we investigate the closure property ofH-tensors under the Hadamard product. It is shown that the Hadamard products of Had...

In this note we utilize a non-trivial block approach due to M. Petrescu to exhibit a Butson-type complex Hadamard matrix of order 19, composed of sixth roots of unity. 1 A new Butson-type complex Hadamard matrix A complex Hadamard matrix H is an n × n complex matrix with unimodular entries such that HH∗ = nIn, where ∗ denotes the Hermitian adjoint and In is the identity matrix of order n. Throu...

1 Hadamard matrices in Space Communications One hundred years ago, in 1893, Jacques Hadamard 21] found square matrices of orders 12 and 20, with entries 1, which had all their rows (and columns) orthogonal. These matrices, X = (x ij), satissed the equality of the following inequality jdet Xj 2 n i=1 n X j=1 jx ij j 2 and had maximal determinant. Hadamard actually asked the question of matrices ...

Hadamard matrices are useful in Hadamard transform spectroscopy and in the construction of optimal chemical designs.'-8 The use of these matrices in spectroscopy has led to the advent of Hadamard transform spectroscopy3 which employs spectroscopic multiplexing techniques and is a powerful tool for the analysis of complex spectra. Besides Hadamard matrices are useful in chemical designs and bloc...