Representation of Markov Functions by Minimal Polynomials over a Finite Field

The method of representing Markov functions with minimal characteristic polynomials over a finite field is proposed. These polynomials are defined on the basis of integrated stochastic matrices. The representation accuracy of stochastic matrices is linearly dependent on the minimum degree of the polynomials. The algorithmic implementation of the method is shown to build a sequence of the Markov functions class considered, with a given linear complexity.