finitely generated extension field

Generators of separably generated field extensions

可分生成域扩张的生成元

Based on the construct idea of prime codes and the transformation relation between finite ground fields and finite extension fields,the construction of concatenated prime codes was analyzed in polynomials form and the finite field model was deduced.

基于素数码的构造思想和有限基域与有限扩域的变换关系,通过分析级联素数码构造过程的多项式表示,得出级联素数码的有限域模型,表明级联素数码是以某一类二次既约多项式为模的有限扩域域乘法某种变形的结果,将级联素数码的构造与有限扩域域乘法相关联,并基于此得出确定级联素数码码族个数的规律。