We consider the question of determining the maximum number of 𝔽q -rational points that can lie on a hypersurface of a given degree in a weighted projective space over the finite field 𝔽q, or in other words, the maximum number of zeros that a weighted homogeneous polynomial of a given degree can have in the corresponding weighted projective space over 𝔽q. In the case of classical projective spaces, this question has been answered by J.-P. Serre. In the case of weighted projective spaces, we give some conjectures and partial results. Applications to coding theory are included and an appendix providing a brief compendium of results about weighted projective spaces is also included.
CITATION STYLE
Aubry, Y., Castryck, W., Ghorpade, S. R., Lachaud, G., O’Sullivan, M. E., & Ram, S. (2017). Hypersurfaces in Weighted Projective Spaces Over Finite Fields with Applications to Coding Theory. In Association for Women in Mathematics Series (Vol. 9, pp. 25–61). Springer. https://doi.org/10.1007/978-3-319-63931-4_2
Mendeley helps you to discover research relevant for your work.