Binary matrices with specified properties

✍ Scribed by V.K. Bhargava

• Publisher: Elsevier Science
• Year: 1977
• Tongue: English
• Weight: 316 KB
• Volume: 303
• Category: Article
• ISSN: 0016-0032
• DOI: 10.1016/0016-0032(77)90132-6

✦ Synopsis

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. A" = Z, 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 x p circulant matrices is isomorphic to the algebra of polynomials modulo (XP-1).