Circulant matrices of each rank over finite fields

Wei, Yangjiang; Zou, Yi Ming

doi:10.22108/toc.2025.138779.2097

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	Circulant matrices of each rank over finite fields
Transactions on Combinatorics
دوره 15، شماره 4، اسفند 2026، صفحه 235-250 اصل مقاله (545.53 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22108/toc.2025.138779.2097
نویسندگان
Yangjiang Wei¹؛ Yi Ming Zou^* ²
¹School of Mathematics and Statistics, Nanning Normal University, and Center for Applied Mathematics of Guangxi at Nanning Normal University, Nanning, P. R. China
²Department of Mathematical Sciences, University of Wisconsin, Milwaukee, USA
چکیده
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.
کلیدواژه‌ها
Circulant matrices؛ finite fields؛ orders of group elements

مراجع
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Circulant matrices of each rank over finite fields