  This paper considers some random processes of the form X_{n+1}=TX_n+B_n (mod
p) where B_n and X_n are random variables over (Z/pZ)^d and T is a fixed d x d
integer matrix which is invertible over the complex numbers. For a particular
distribution for B_n, this paper improves results of Asci to show that if T has
no complex eigenvalues of length 1, then for integers p relatively prime to
det(T), order (log p)^2 steps suffice to make X_n close to uniformly
distributed where X_0 is the zero vector. This paper also shows that if T has a
complex eigenvalue which is a root of unity, then order p^b steps are needed
for X_n to get close to uniform where b is a value which may depend on T and
X_0 is the zero vector.

Probability