Circulant matrices of each rank over finite fields
نویسندگان
1 Department of Mathematical Sciences, University of Wisconsin, Milwaukee, USA
2 School of Mathematics and Statistics, Nanning Normal University, and Center for Applied Mathematics of Guangxi at Nanning Normal University, Nanning, P. R. China
doi
10.22108/toc.2025.138779.2097چکیده
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.
