Automatic Control and Computer Sciences

, Volume 48, Issue 4, pp 214–220

Generalized Mersenne matrices and Balonin’s conjecture

Article

DOI: 10.3103/S0146411614040063

Cite this article as:
Sergeev, A.M. Aut. Control Comp. Sci. (2014) 48: 214. doi:10.3103/S0146411614040063
  • 30 Downloads

Abstract

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.

Keywords

information processing compression masking orthogonal matrices quasi-orthogonal matrices Hadamard matrices Belevitch matrices Mersenne numbers Fermat numbers Euler-Fermat criterion 

Copyright information

© Allerton Press, Inc. 2014

Authors and Affiliations

  1. 1.St. Petersburg State University of Aerospace InstrumentationSt. PetersburgRussia

Personalised recommendations