Morrison and Pinkham [4] gave a characterization of the semigroups of Galois Weierstrass points, i.e., total ramification points of cyclic coverings of the projective line of degree n. They showed that such a semigroup must satisfy certain equalities, which we call the M-P equalities in this paper, and that the converse holds for any prime n % 7. In this paper we consider the case when n is a prime number p^11. For each prime p^11, we give a semigroup which satisfies the M-P equalities but is not the semigroup of a Galois Weierstrass point. For this, we study the semigroups of Galois Weierstrass points using the equations defining curves which are cyclic covering of the projective line.
We prove that there does not exist a [q 4 + q 3 − q 2 − 3q − 1, 5, q 4 − 2q 2 − 2q + 1] q code over the finite field F q for q ≥ 5. Using this, we prove that there does not exist a [g q (5, d), 5, d] q code with q 4 − 2q 2 − 2q + 1 ≤ d ≤ q 4 − 2q 2 − q for q ≥ 5, where g q (k, d) denotes the Griesmer bound.MSC 2000: 94B65, 94B05, 51E20, 05B25
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