有限域上二元线性码的一个构造

A construction of binary linear codes in finite fields

在有限域F8上定义码C,证明了码C是参数为[8,4,4]的八元线性码;由线性码C构造码G,确定了码G的码长,维数和最小距离,证明码G是参数[40,20,8]的二元线性码.

A code C is defined in the finite fields over Fs. It is proved that code C is an octa-element linear code over F~ with parameters [8,4,4-1. A code G is constructed through code C, its code length, dimension and minimum distance are determined, and it is proved that code G is a binary linear code with parameters 1-40, 20, 8-1.