39 citations · 311 across the 30 of their papers we have counts for
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Hyperplane Sections of Determinantal Varieties over Finite Fields and Linear Codes
Peter Beelen, Sudhir R. Ghorpade
We determine the number of -rational points of hyperplane sections of classical determinantal varieties defined by the vanishing of minors of a fixed size of a gene…
A Combinatorial Approach to the Number of Solutions of Systems of Homogeneous Polynomial Equations over Finite Fields
Peter Beelen, Mrinmoy Datta, Sudhir R. Ghorpade
We give a complete conjectural formula for the number of maximum possible -rational points on a projective algebraic variety defined by linearly indep…
A Note on Nullstellensatz over Finite Fields
Sudhir R. Ghorpade
We give an expository account of Nullstellensatz-like results when the base field is finite. In particular, we discuss the vanishing ideal of the affine space and of the projective…
Vanishing ideals of projective spaces over finite fields and a projective footprint bound
Peter Beelen, Mrinmoy Datta, Sudhir R. Ghorpade
We consider the vanishing ideal of a projective space over a finite field. An explicit set of generators for this ideal has been given by Mercier and Rolland. We show that these ge…