We obtain certain algebraic invariants relevant in studying codes on subgroups of weighted
projective tori inside an n-dimensional weighted projective space. As application, we …

Motivated by applications to the theory of error-correcting codes, we give an algorithmic
method for computing a generating set for the ideal generated by $\beta $-graded …

We show that the number of rational points of a subgroup inside a toric variety over a finite
field defined by a homogeneous lattice ideal can be computed via Smith normal form of the …

Toric codes are examples of evaluation codes. They are produced by evaluating
homogeous polynomials of a fixed degree at the F q-rational points of a subset Y of a toric …

Let X be a complete simplicial toric variety over a finite field with a split torus TX. For any
matrix Q, we are interested in the subgroup YQ of TX parameterized by the columns of Q. We …

Let X be a complete n-dimensional simplicial toric variety over a finite field with
homogeneous coordinate ring S. In this survey, we review algebraic methods for studying …

Weighted projective spaces are natural generalizations of projective spaces with a rich
structure. Projective Reed-Muller codes are error-correcting codes that played an important …

Let $ K $ be a finite field and $ X $ be a complete simplicial toric variety over $ K $ with split
torus $ T_X\cong (K^*)^ n $. We give an algorithm relying on elimination theory for finding …

Toric codes are examples of evaluation codes produced by evaluating homogeous
polynomials of a fixed degree $\alpha $ at the $\F_q $-rational points of a subset $ Y $ of a …

Weighted projective spaces are natural generalizations of projective spaces with a rich
structure. Projective Reed-Muller codes are error-correcting codes that played an important …