Synthesis of symmetrical functions of golden ratio - Белецкий, Анатолий Яковлевич; Лужецкий, Владимир Андреевич (Ukrainian Information Security Research Journal, 2016)
The article deals with the formation of symmetric Walsh-like systems functions of the golden ratio (FGR) binary-power order. The basis of the construction of systems FGR on the method of Kronecker product, which is used in the synthesis of the Walsh-Kronecker systems. Generating matrix for the Walsh-Kronecker systems is the Hadamard matrix of the second order, in which the element is substituted with an element -1 on -α, equal to the ratio of the golden ratio. Algorithms direct preparation systems FGR arbitrary binary-power order, similar to the Walsh-Hadamard and Walsh-Paley. Synthesis of the full set of symmetrical systems FGR carried permutation of basic functions systems, the Walsh-Paley. Rules permutation function sets the indicator matrix of the corresponding systems. Nondegenerate indicator is symmetrical with respect to the field of auxiliary diagonal (0,1) matrix, where in the weight of each column (as rows) of the matrix, equal to the sum of ones, must be an odd number.