Weighted projective spaces are natural generalizations of classical projective spaces having rich structures and exhibiting interesting algebraic geometric properties. They have been regarded as convenient ambient spaces to create interesting classes of linear codes over finite fields in the literature (see, [1],[2],[3]). Weighted Projective Reed--Muller codes were introduced by S{\o}rensen in [3]. The purpose of this talk is to introduce these codes over a finite field, to give results for their main parameters, and to reveal the role of computer algebra packages to study some of the relevant combinatorial commutative algebraic invariants. We pay a particular attention on two dimensional case to obtain more explicit information about the minimal free resolution of the vanishing ideal of the weighted projective plane $\mathbb{P}(1,a,b)$ over $\mathbb{F}_q$. This yields to the Hilbert function giving the dimension of the code and regularity index which is crucial to eliminate trivial codes.
Keywords: algebraic invariants, weighted projective spaces, error-correcting codes, toric codes.