2017/01/01 by Yves Aubry, Wouter Castryck, Sudhir R. Ghorpade +4 · 6 citations
Computer Science · Engineering · Mathematics · #Coding theory and cryptography #Combinatorics #Degree (music) #Discrete mathematics #Finite Group Theory Research #Finite field #Homogeneous #Hypersurface #Mathematics #Physics #Projective space #Projective test #Pure mathematics #cs.IT #graph theory and CDMA systems #math.AG #math.IT
paper · pdf · doi:10.1007/978-3-319-63931-4_2
published in Association for Women in Mathematics series, 25-61 (Springer International Publishing)
openalex publication_date 2017/01/01 · arxiv created 2017/06/09 · arxiv updated 2018/01/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We consider the question of determining the maximum number of \mathbbFq-rational points that can lie on a hypersurface of a given degree in a weighted projective space over the finite field \mathbbFq, 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 \mathbbFq. 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.