Dragan Jankovic, Radomir S. Stankovic and Claudio Moraga

This paper discusses methods for efficient implementation of algorithms for determination of Fixed-polarity Galois field (FPGF) expressions for q -valued logic functions (-prime). Calculations of coefficients in FPGF expressions can be most efficiently performed in terms of space and time, if conversion of an expression for a given polarity into the expression for another polarity is done along the so-called extended dual polarity route. However, there are many possible extended dual polarity routes which differ in the associated processing rules. The complexity of whatever soft-ware or hardware resources required for calculations of FPGF expressions depends on the number of different processing rules required along a route. In this paper, we introduce the notion of homogeneous extended dual polar-ity routes and show that calculations along these routes can be performed with a reduced number of processing rules required. Due to that, both hard-ware and software implementation of the procedure for determination of all possible FPGF expressions for a given function is considerably simplified.