Generalized Mersenne matrices and Balonin’s conjecture
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- Sergeev, A.M. Aut. Control Comp. Sci. (2014) 48: 214. doi:10.3103/S0146411614040063
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Properties of generalized Hadamard matrices and a conjecture on the existence of Mersenne matrices included into the former are discussed. A new classification of few-level quasi-orthogonal matrices, including matrices of even and odd orders, is presented. Matrices of Euler, Mersenne, and Hadamard are considered. The fundamental differences between the matrices of Mersenne and Fermat, which explain the failure of the proof of the Hadamard conjecture, are shown.