Vanishing Ideals over Finite Fields
Azucena Tochimani, Rafael H. Villarreal · Mathematical Notes · 2019
Let $$\mathbb{F}_{q}$$ F q be a finite field, let $$\mathbb{X}$$ X be a subset of the projective space ℙs−1 over $$\mathbb{F}_{q}$$ F q parametrized by rational functions, and let I( $$(\mathbb{X})$$ ( X ) ) be the vanishing ideal of $$\mathbb{X}$$ X . The main result of this paper is a formula for I( $$(\mathbb{X})$$ ( X ) ) that will allow us to compute (i) the algebraic invariants of I( $$(\mathbb{X})$$ ( X ) ) and (ii) the basic parameters of the corresponding Reed–Muller-type code.