39 citations · 311 across the 30 of their papers we have counts for
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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…
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…
Hypersurfaces in weighted projective spaces over finite fields with applications to coding theory
Yves Aubry, Wouter Castryck, Sudhir R. Ghorpade +3
We consider the question of determining the maximum number of -rational points that can lie on a hypersurface of a given degree in a weighted projective space over th…
Maximum Number of Common Zeros of Homogeneous Polynomials over Finite Fields
Peter Beelen, Mrinmoy Datta, Sudhir R. Ghorpade
About two decades ago, Tsfasman and Boguslavsky conjectured a formula for the maximum number of common zeros that linearly independent homogeneous polynomials of degree in…
Remarks on Tsfasman-Boguslavsky Conjecture and Higher Weights of Projective Reed-Muller Codes
Mrinmoy Datta, Sudhir R. Ghorpade
Tsfasman-Boguslavsky Conjecture predicts the maximum number of zeros that a system of linearly independent homogeneous polynomials of the same positive degree with coefficients in…
Number of Solutions of Systems of Homogeneous Polynomial Equations over Finite Fields
Mrinmoy Datta, Sudhir R. Ghorpade
We consider the problem of determining the maximum number of common zeros in a projective space over a finite field for a system of linearly independent multivariate homogeneous po…