Abstract
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.
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Tochimani, A., Villarreal, R.H. Vanishing Ideals over Finite Fields. Math Notes 105, 429–438 (2019). https://doi.org/10.1134/S0001434619030131
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DOI: https://doi.org/10.1134/S0001434619030131