  The aim of this paper is to study the correlation properties of random
sequences with additive linear conditional probability distribution function
(CPDF) and elaborate a reliable tool for their generation. It is supposed that
the state space of the sequence under examination belongs to a finite set of
real numbers. The CPDF is assumed to be additive and linear with respect to the
values of the random variable. We derive the equations that relate the
correlation functions of the sequence to the memory function coefficients,
which determine the CPDF. The obtained analytical solutions for the equations
connecting the memory and correlation functions are compared with the results
of numerical simulation. Examples of possible correlation scenarios in the
high-order additive linear chains are given.
