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- W2780505258 abstract "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&t(q)<1.835sqrt{qln q}.end{align*} The new bounds are used to increase regions of pairs $(N,q)$ for which it is proved that every normal rational curve in $mathrm{PG}(N,q)$ is a complete $(q+1)$-arc or, equivalently, that no $[q+1,N+1,q-N+1]_q$ generalized doubly-extended Reed-Solomon code can be extended to a $[q+2,N+1,q-N+2]_q$ MDS code." @default.
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- W2780505258 date "2016-09-19" @default.
- W2780505258 modified "2023-09-27" @default.
- W2780505258 title "On Almost Complete Subsets of a Conic in $mathrm{PG}(2,q)$, Completeness of Normal Rational Curves and Extendability of Reed-Solomon Codes" @default.
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