Vanishing ideals over finite fields

Azucena Tochimani; Rafael H. Villarreal

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arXiv · 1502.05451

Vanishing ideals over finite fields

Azucena Tochimani·Rafael H. Villarreal

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Abstract

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.

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BibTeX RIS

Azucena Tochimani, Rafael H. Villarreal. 2015-02-19. Vanishing ideals over finite fields. https://arxiv.org/abs/1502.05451

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