Circulant matrices of each rank over finite fields

We consider the enumeration of circulant matrices over a finite field with q elements, and we provide formulas to compute the number of these circulant matrices for each rank. We also consider the computation of the orders of q in multiplicative groups of integers modulo n that are needed in the enumeration, and we give a reduction method to compute these orders. We then use these results to derive explicit formulas for the enumerations of infinite sequences of circulant matrices of some special types.

کلیدواژه ها:

Circulant Matrices ، finite fields ، orders of group elements