Let I be a graded ideal of a standard graded polynomial ring S with coefficients in a field K.
The asymptotic behaviour of the v-number of the powers of I is investigated. Natural lower …

Motivated by notions from coding theory, we study the generalized minimum distance (GMD)
function δ I (d, r) of a graded ideal I in a polynomial ring over an arbitrary field using …

The aim of this work is to study the dual and the algebraic dual of an evaluation code using
standard monomials and indicator functions. We show that the dual of an evaluation code is …

We study the subfield subcodes of projective Reed–Solomon codes and their duals: we
provide bases for these codes and estimate their parameters. With this knowledge, we can …

Evaluation Codes Associated to Complete Bipartite Graphs 1 Introduction Page 1 International
Journal of Algebra, Vol. 2, 2008, no. 4, 163 - 170 Evaluation Codes Associated to Complete …

In this paper we give a formula for the second generalized Hamming weight of certain
evaluation codes arising from a projective torus. This allows us to compute the …

Abstract For projective Reed–Muller-type codes we give a global duality criterion in terms of
the v-number and the Hilbert function of a vanishing ideal. As an application, we provide a …

Let $ I $ be a graded ideal of a standard graded polynomial ring $ S $ with coefficients in a
field $ K $. The asymptotic behaviour of the $\text {v} $-number of the powers of $ I $ is …

Abstract Evaluation codes have been studied since some years ago. At the very beginning
they were called projective Reed-Muller type codes and their main parameters (length …

In this paper we define the evaluation codes associated to some specific matrices which are
related to toric varieties. We compute the main parameters of these codes: the length, the …