Mathematical Notes

, Volume 105, Issue 3–4, pp 429–438 | Cite as

Vanishing Ideals over Finite Fields

  • A. TochimaniEmail author
  • R. H. VillarrealEmail author


Let \(\mathbb{F}_{q}\) be a finite field, let \(\mathbb{X}\) be a subset of the projective space ℙs−1 over \(\mathbb{F}_{q}\) parametrized 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 allow us to compute (i) the algebraic invariants of I(\((\mathbb{X})\)) and (ii) the basic parameters of the corresponding Reed–Muller-type code.


vanishing ideal rational parametrization finite field Reed–Muller-type code 


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© Pleiades Publishing, Ltd. 2019

Authors and Affiliations

  1. 1.Mathematics Department of Center for Research and Advanced StudiesNational Polytechnic InstituteMexico CityMexico

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