几何Goppa码的最小距离

The minimum distance of Geometric Goppa codes

对于具有生成多项式Ｇ（ｘ）的二元Ｇｏｐｐａ码，令（ｘ）是能被Ｇ（ｘ）整除的最低次完全平方多项式，则其最小距离．文中首先在几何Ｇｏｐａ码Ｃ（Ｄ，Ｇ）中得到了相应的结果；其次还得到几何Ｇｏｐｐａ码Ｃ（Ｄ，Ｇ）最小距离扩张的一般性定理．

For Goppa code with the generating polynomialg(x),let g(x)be the lowest degree per-fect square which is diruible by g(x).Then d≥eg(g(x))+1,where d is the minimum dis-ance of this code.In this paper,we generalize this result to Geometric Goppa code.We alsoget a general extension theorem for minimum distance in Geometric Goppa code.