Mathematics – Algebraic Geometry
Scientific paper
2011-04-28
Journal of the Indian Institute of Science, Vol.91 No.1 (Jan-March 2011)
Mathematics
Algebraic Geometry
30 pages, presented at CAAG 2010 (Bangalore, India)
Scientific paper
In this paper we treat several topics regarding numerical Weierstrass semigroups and the theory of Algebraic Geometric Codes associated to a pair $(X, P)$, where $X$ is a projective curve defined over the algebraic closure of the finite field $F_q$ and P is a $F_q$-rational point of $X$. First we show how to evaluate the Feng-Rao Order Bound, which is a good estimation for the minimum distance of such codes. This bound is related to the classical Weierstrass semigroup of the curve $X$ at $P$. Further we focus our attention on the question to recognize the Weierstrass semigroups over fields of characteristic 0. After surveying the main tools (deformations and smoothability of monomial curves) we prove that the semigroups of embedding dimension four generated by an arithmetic sequence are Weierstrass.
Oneto Anna
Padrone Alessio Del
Tamone Grazia
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