Interrelation of Symmetry and Antisymmetry of Quasi-Orthogonal Cyclic Matrices with Prime Numbers

Quasi-orthogonal Hadamard matrices and Mersenne with two three values of the elements, used in digital data processing, are considered, as well basis error-correcting codes algorithms for transforming orthogonal images. Attention is paid to structures cyclic symmetries antisymmetries. The connection between symmetry antisymmetry on a orders equal prime numbers, products close primes, composite powers number shown. Separately, degrees 2 distinguished, both block element values. It shown that symmetric bicyclic structures, according extended Riser boundary, do not exist above 32. belonging sequence numbers 2k ‒ 1 nested main family 4t antisymmetric form. For number, form block-diagonal constructions value power determines blocks along diagonal matrix which elements third located. symmetrical antisymmetric.