Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the minimum distance of AG codes, on Weierstrass semigroups and the
  smoothability of certain monomial curves in 4-Space   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.

18
The categories of this paper are: econ
4
The categories of this paper are: cond-mat
0
The categories of this paper are: hep-ph
29
The categories of this paper are: funct-an
28
The categories of this paper are: alg-geom
17
The categories of this paper are: q-fin
19
The categories of this paper are: eess
20
The categories of this paper are: acc-phys
31
The categories of this paper are: ao-sci
16
The categories of this paper are: stat
26
The categories of this paper are: bayes-an
35
The categories of this paper are: mtrl-th
1
The categories of this paper are: cs
33
The categories of this paper are: plasm-ph
24
The categories of this paper are: dg-ga
6
The categories of this paper are: astro-ph