On complete m-arcs

03/23/2023

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by   Luca Bastioni, et al.

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Let m be a positive integer and q be a prime power. For large finite base fields 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.