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Azucena Tochimani

Publications and source records attributed to Azucena Tochimani.

4 recordsLinked to original sources
arXiv2016

Vanishing ideals over finite fields

Let $\mathbb{F}_q$ be a finite field, let $\mathbb{X}$ be a subset of a projective space ${\mathbb P}^{s-1}$, over the field $\mathbb{F}_q$, parameterized by rational functions, and let $I(\mathbb{X})$ be the vanishing ideal of $\mathbb{X}$. The main result of this paper is a formula for $I(\mathbb{X})$ that will allows us to compute: (i) the algebraic invariants of $I(\mathbb{X})$, and (ii) the basic parameters of the corresponding Reed-Muller-type code.

math.AC↗
arXiv2016

Direct products in projective Segre codes

Let K=Fq be a finite field. We introduce a family of projective Reed-Muller-type codes called projective Segre codes. Using commutative algebra and linear algebra methods, we study their basic parameters and show that they are direct products of projective Reed-Muller-type codes. As a consequence we recover some results on projective Reed-Muller-type codes over the Segre variety and over projective tori.

math.AC↗
arXiv2015

Binomial vanishing ideals

In this paper we characterize, in algebraic and geometric terms, when a graded vanishing ideal is generated by binomials over any field K.

math.AC↗