On complete $m$-arcs

Luca Bastioni; Giacomo Micheli

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arXiv · 2303.13670

On complete $m$-arcs

Luca Bastioni·Giacomo Micheli

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Abstract

Let $m$ be a positive integer and $q$ be a prime power. For large finite base fields $\mathbb F_q$, we show that any curve can be used to produce a complete $m$-arc as long as some generic explicit geometric conditions on the curve are verified. To show the effectiveness of our theory, we derive complete $m$-arcs from hyperelliptic curves and from Artin-Schreier curves.

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Luca Bastioni, Giacomo Micheli. 2023-03-23. On complete $m$-arcs. https://arxiv.org/abs/2303.13670

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