  We call Krawtchouk-Griffiths systems, KG-systems, systems of multivariate
polynomials orthogonal with respect to corresponding multinomial distributions.
The original Krawtchouk polynomials are orthogonal with respect to a binomial
distribution. Here we present a Fock space construction with raising and
lowering operators. The operators of "multiplication by X" are found in terms
of boson operators and corresponding recurrence relations presented. The
Riccati partial differential equations for the differentiation operators,
Berezin transform and associated partial differential equations are found.
These features provide the specifications for a Bernoulli system as a
quantization formulation of multivariate Krawtchouk polynomials.
