Impulse response arrays of discrete-space systems over a finite field

The main thrust of this paper is directed towards an analysis of the structure and properties of the impulse response array of two-dimensional (2-D) discrete-space systems, characterizable by rational functions having coefficients in a field Zq. It is shown that such an array exhibits a row (column) type of periodicity. Expressions for the period are derived. Arrays with a maximum of three levels in the auto-correlation function are identified and explicit expressions for these levels are given.