计算Weierstrass半群及奇异平面模型上的Feng-Rao距离

Further improvements on the Feng-Rao bound for dual codes

Salazar, Dunn and Graham in [Salazar et. al., 2006] presented an improved Feng-Rao bound for the minimum distance of dual codes. In this work we take the improvement a step further. Both the original bound by Salazar et. al., as well as our improvement are lifted so that they deal with generalized Hamming weights. We also demonstrate the advantage of working with one-way well-behaving pairs rather than weakly well-behaving or well-behaving pairs.

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 …

On the parameters of Algebraic Geometry codes related to Arf semigroups

In this paper we compute the order (or Feng-Rao) bound on the minimum distance of one-point algebraic geometry codes, when the Weierstrass semigroup at the point Q is an Arf semigroup. The results developed to that purpose also provide the dimension of the improved geometric Goppa codes related to those.

平面曲线的符号Hamburger-Noether表达式与AG码的构造

Symbolic Hamburger-Noether expressions of plane curves and construction of AG codes

本文提出基于符号Hamburger-Noether表达式的算法，计算有理除子空间基和Weierstrass半群，用于代数几何码的构造与译码。