Abstract
Quasi-orthogonal Hadamard matrices and Mersenne matrices with two element values are considered, which are used in digital data processing, orthogonal image transformations, and also as a basis for error-correcting codes. Attention is paid to the structures of cyclic matrices with symmetries and antisymmetries. The relationship between symmetry and antisymmetry of structures of cyclic matrices on orders equal to prime numbers, product of close prime numbers, composite numbers, powers of a prime number is shown. Separately, the orders equal to the power of the prime number 2, both the orders of the Hadamard matrices and the basis of the composite orders of the Mersenne matrices of block structures with two element values, are singled out separately.
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