Abstract: 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.