The study of generators of orthogonal pseudo-random sequences

Abstract

The paper deals with the features of construction and search of two cyclic Hadamard matrices, whose implementation variants are characterized by non-symmetry of one of the two blocks of the matrix structure. The basis of their construction is the analytical theory of difference equations based on Fermat–Euler theorem. A numerical method for finding two cyclic blocks, which are the basis for the construction of Hadamard matrices, is developed. This method accelerates a trivial search of the desired sequence, thus distributing them in different bins. The method implementation uses a hash function. As a result, a wide set of new Hadamard matrices was found. New versions of Hadamard matrices of orders 100 and 116 were also obtained.