Abstract
Let X be a smooth curve of genus g defined over \(\mathbb {F}_q\). In this note we study the maximal number of points \(P_1,\ldots ,P_n\in X(\mathbb {F}_q)\) such that \(h^0(\mathcal {O}_X(a_1P_1+\cdots +a_nP_n)) =1\) for all \((a_1,\ldots ,a_n)\in {\mathbb {N}_0} ^n\) with \(a_1+\cdots +a_n \le g\). We also look at the Weierstrass n-semigroup of n points of \(X(\mathbb {F}_q)\) when \(n>q\).
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The author was partially supported by MIUR and GNSAGA of INdAM (Italy).
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Communicated by J. W. P. Hirschfeld.
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Ballico, E. Non-special subsets of the set of points of a curve defined over a finite field. Des. Codes Cryptogr. 80, 453–457 (2016). https://doi.org/10.1007/s10623-015-0112-4
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DOI: https://doi.org/10.1007/s10623-015-0112-4