级联素数码的有限域模型

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．上述结果对研究将素数码的构造思想扩展到有限扩域具有启发意义,为基于素数码构造周期更长、序列数目更多的跳频序列族提供了一条新的思路．

Finite field model of concatenated prime codes

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.The model indicates that concatenated prime codes are the result of a little change of finite extension field multiplication with one certain class of quadratic irreducible polynomials.This result associates the construct of concatenated prime codes to the multiplication of finite extension fields similarly to that of prime codes to the finite ground fields.Furthermore,according to the conclusion above,one rule is achieved to decide the groups' number of concatenated prime codes.These two conclusions are theoretically enlightening to extend the construct idea of prime codes to finite extension fields.And a new way is provided to construct frequency hopping sequences with longer period and more sequences based on prime codes.