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 IF. A criteria is given for determining a minimal subset of semigroup elements which generate such a semigroup where 2 ≤ m ≤ | IF |. For all 2 ≤ m ≤ q + 1, we determine the Weierstrass semigroup of any m-tuple of collinear IF q 2-rational points on a Hermitian curve y q + y = x q+1.
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