Abstract
We examine the structure of the Weierstrass semigroup of an m-tuple of points on a smooth, projective, absolutely irreducible curve X over a finite field \(\mathbb{F}\). A criteria is given for determining a minimal subset of semigroup elements which generate such a semigroup where 2 \( \leq m \leq |\mathbb{F}|\). For all 2 mq + 1, we determine the Weierstrass semigroup of any m-tuple of collinear \(\mathbb{F}_{q^2}\)-rational points on a Hermitian curve y q + y = x q + 1.
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© 2004 Springer-Verlag Berlin Heidelberg
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Matthews, G.L. (2004). The Weierstrass Semigroup of an m-tuple of Collinear Points on a Hermitian Curve. In: Mullen, G.L., Poli, A., Stichtenoth, H. (eds) Finite Fields and Applications. Fq 2003. Lecture Notes in Computer Science, vol 2948. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24633-6_2
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DOI: https://doi.org/10.1007/978-3-540-24633-6_2
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-21324-6
Online ISBN: 978-3-540-24633-6
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