  We define weighted projective Reed-Muller codes over a subset of weighted
projective space over a finite field. We focus on the case when the set X is a
projective weighted torus. We show that the vanishing ideal of X is a lattice
ideal and relate it with the lattice ideal of a minimal presentation of the
semigroup algebra of Q, the numerical semigroup generated by the weights of the
projective space. We compute the index of regularity of the vanishing ideal as
function of the weights and the Frobenius number of Q. We compute the basic
parameters of weighted projective Reed-Muller codes over a 1-dimensional
weighted torus and prove they are maximum distance separable codes.
