  Let K be a finite field and let X* be an affine algebraic toric set
parameterized by monomials. We give an algebraic method, using Groebner bases,
to compute the length and the dimension of C_X*(d), the parameterized affine
code of degree d on the set X*. If Y is the projective closure of X*, it is
shown that C_X^*(d) has the same basic parameters that C_Y(d), the
parameterized projective code on the set Y. If X* is an affine torus, we
compute the basic parameters of C_X*(d). We show how to compute the vanishing
ideals of X* and Y.
