Weight distributions of geometric Goppa codes
Weight distributions of geometric Goppa codes
复制标题
几何 Goppa 码的权重分布
DOI：
10.1090/s0002-9947-99-02179-0
复制
发表时间：
1999
影响因子：
1.3
通讯作者：
I. Duursma
中科院分区：
文献类型：
--
作者：
I. Duursma
Goppa在80年代初定义了一类特殊的代数几何码，并考虑了计算线性码的重量分布的一般困难问题。已知的结果限制从椭圆曲线的代码。我们通过用L-级数表示权分布，得到了高亏格曲线的结果。给出了权分布的一般性质、权分布的描述和计算方法，并给出亏格为2和亏格为3的曲线的例子。
The in general hard problem of computing weight distributions of linear codes is considered for the special class of algebraic-geometric codes, defined by Goppa in the early eighties. Known results restrict to codes from elliptic curves. We obtain resullts for curves of higher genus by expressing the weight distributions in terms of L-series. The results include general properties of weight distributions, a method to describe and compute weight distributions, and worked out examples for curves of genus two and three.