检错码的对偶定理

自动请求重传(ARQ)方法已经在许多数字通信系统特别是通信网中获得了广泛的应用。在ARQ系统中,分组码的不可检错误概率是决定系统性能的重要参数,因此研究各种线性分组码的不可检错误概率显得非常重要。在本文中,不可检错误概率满足上限q~(-(m-k))的q进制线性分组码被定义为检错好码。笔者证明了关于检错码的一个对偶定理,即GF(q)上(n,k)线性分组码为检错好码的充要条件是其对偶码也是检错好码。对偶定理表明,可以从一个线性分组码的对偶码研究它的检错能力,本文用这个定理得到了关于检错码的一系列新的结论。

A Dual Theorem on Error Detection Codes

Automatic repeat request (ARQ) schemes have been widely applied to many digital communication systems,especially,computer communication networks. Because the undetected error probability of block codes is a key parameter determining the performance of ARQ systems.it is important to deal with the undetected error probability of a variety of linear block codes. A linear block code, of q-al system whose undetected error probability satisfies the upper bound q-(m-k), is defined as a good code for error detection. A dual theorem on error detection codes is shown,that is ,a (n,k) linear block code in GF(q) is the good code for error detection if and only if its dual code (n,n - k) is also a good one. Therefore,the error detection capability of linear block codes can be known through their dual codes. A series of new results on error detection codes are obtained with the help of the dual theorem.