On complete m-arcs

2023/03/23 by Bastioni, Luca, Micheli, Giacomo
#05B25 #11R45 #11T06 #51E20 #51E21 #Combinatorics (math.CO) #FOS: Computer and information sciences #FOS: Mathematics #Information Theory (cs.IT) #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2303.13670

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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