On Almost Complete Subsets of a Conic in $\mathrm{PG}(2,q)$, Completeness of Normal Rational Curves and Extendability of Reed-Solomon Codes
Daniele Bartoli, Alexander A. Davydov, Stefano Marcugini, Fernanda Pambianco · arXiv (Cornell University) · 2016
A subset $\mathcal{S}$ of a conic $\mathcal{C}$ in the projective plane $\mathrm{PG}(2,q)$ is called almost complete (AC-subset for short) if it can be extended to a larger arc in $\mathrm{PG}(2,q)$ only by the points of $\mathcal{C}\setminus \mathcal{S}$ and by the nucleus of $\mathcal{C}$ when $q$ is even. New upper bounds on the smallest size $t(q)$ of an AC-subset are obtained, in particular, \begin{align*} &t(q)