Vanishing ideals of projective spaces over finite fields and a projective footprint bound
DOI10.1007/s10114-018-8024-7zbMath1411.14024arXiv1801.09139OpenAlexW2963116074WikidataQ129066244 ScholiaQ129066244MaRDI QIDQ1734904
Mrinmoy Datta, Sudhir R. Ghorpade, Beelen, Peter
Publication date: 27 March 2019
Published in: Acta Mathematica Sinica. English Series (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1801.09139
Gröbner basisfinite fieldprojective spacealgebraic varietyvanishing idealprojective hypersurfacefootprint bound
Rational points (14G05) Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) (13P10) Polynomials over finite fields (11T06) Finite ground fields in algebraic geometry (14G15) Varieties over finite and local fields (11G25)
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Cites Work
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- Decoding affine variety codes using Gröbner bases
- Homogeneous polynomials vanishing on the projective space \(\mathbb{P}^m(\mathbb{F}_q)\)
- Generalized Hamming weights of affine Cartesian codes
- Equations et variétés algébriques sur un corps fini
- Generalized minimum distance functions
- Projective nested Cartesian codes
- Relative generalized Hamming weights of \(q\)-ary Reed-Muller codes
- On a conjecture of Tsfasman and an inequality of Serre for the number of points on hypersurfaces over finite fields
- An upper bound on the number of rational points of arbitrary projective varieties over finite fields
- Maximum Number of Common Zeros of Homogeneous Polynomials over Finite Fields
- Projective Reed-Muller codes
- Generalized Hamming weights of q-ary Reed-Muller codes
- Footprints or generalized Bezout's theorem
- A note on Nullstellensatz over finite fields
- Duals of Affine Grassmann Codes and Their Relatives
- Number of solutions of systems of homogeneous polynomial equations over finite fields