关于Goppa几何码最小距离的一个新方法  

A new approach to the minimum distance of Goppa geometry codes

作　　者：戴林送[1] 胡万宝[1] 

机构地区：[1]安庆师范学院数学系,安徽安庆246011

出　　处：《纯粹数学与应用数学》2007年第4期529-534,539,共7页Pure and Applied Mathematics

基　　金：安徽省教育厅(2006kj240B)

摘　　要：引进一个关于Goppa几何码(代数几何码)最小距离界的一个新方法.应用Maharaj的思想(即用显示基来近似表达Riemann-Roch空间)到Goppa几何码的最小距离的界上去.通过厄米特曲线上的代数几何码的一类例子,来证明标准的几何码的下界在某些情形下可以被显著地改进.进一步地,我们给出了这些码的最小距离上界,并说明了我们的下界非常接近这个上界.A new approach to the bounds of the minimum distance of Goppa geometry codes （algebraic-geometric codes） is presented. We apply Maharaj＇s idea, which use explicit bases to express approximately Riemann-Roch space, to the bounds of the minimum distance of Goppa＇s Geometry codes. Then, by a class of examples from algebraic-geometric codes on Hermitian curves, we show that the Goppa＇s standard lower bound of the codes can be improved significantly in some .cases. We further give the upper bound of the minimum distance of the codes as well, and show that our lower bound is very close to our upper bound.

关 键 词：厄米特曲线 代数几何码 代数函数域 

分 类 号：O157.4[理学—数学]