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We generalize results of Homma and Kim [2001, J. Pure Appl. Algebra 162, 273–290] concerning an improvement on the Goppa bound on the minimum distance of certain Goppa codes.
We classify, up to isomorphism, maximal curves covered by the Hermit-ian curve H by a prime degree Galois covering. We also compute the genus of maximal curves obtained by the quotient of H by… (More)
We determine the Weierstrass semigroup of a pair of rational points on Norm-Trace curves. We use this semigroup to improve the lower bound on the minimum distance of two-point algebraic geometry… (More)
The quality of an algebraic geometry code depends on the curve from which the code has been defined. In this paper we consider codes obtained from Castle curves, namely those whose number of rational… (More)
Previous results on genera g of F q 2-maximal curves are improved: (1) Either g ≤ ⌊(q 2 − q + 4)/6⌋ , or g = ⌊(q − 1) 2 /4⌋ , or g = q(q − 1)/2. (2) The hypothesis on the existence of a particular… (More)
We study geometrical properties of maximal curves having classical Weierstrass gaps.
Hoslashholdt, van Lint, and Pellikaan used order functions to construct codes by means of Linear Algebra and Semigroup Theory only. However, Geometric Goppa codes that can be represented by this… (More)
The order bound for the minimum distance of algebraic geometry codes was originally defined for the duals of one-point codes and later generalized for arbitrary algebraic geometry codes. Another… (More)
Three 2,3,1',3'-tetraacyl- and two 2,3,3'-triacylsucroses, nicandroses A-E (1-5), were isolated from the fruits of Physalis nicandroides var. attenuata. The acyl groups in these new compounds were… (More)
For the Hermitian curve H defined over the finite field Fq2, we give a complete classification of Galois coverings of H of prime degree. The corresponding quotient curves turn out to be special cases… (More)