Binary matrices with specified properties |
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| Authors: | VK Bhargava |
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| Institution: | Department of Electrical Engineering, Concordia University, Montreal, Quebec, Canada |
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| Abstract: | The binary matrices A which are circulant with one or more of the following properties: (1) A is symmetric, i.e. A = AT, (2) A is orthogonal, i.e. AAT = I (mod 2), (3) A has low multiplicative order, i.e. Am = I, occur often in communication, control and network theory problems. In this paper we construct a number of such matrices. The results are based on the theory of power-residues modulo an odd prime p, and the fact that the algebra of all p × p circulant matrices is isomorphic to the algebra of polynomials modulo (xp?1). |
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