Representation of Polynomials Over Finite Fields With Circulants - Muratović, Amela (Sarajevo Journal of Mathematics, 2024)
Representation of polynomials over complex fields is well known. In this paper a similar representation is given for polynomials of degree less than $q-1$, over finite fields. The results are theorems that characterize the centralizer of the circulant of a permutation polynomial, and a formula for the calculation of the determinant of the circulant as the product of the determinants of the polynomials defined on the cosets of some multilpicative subgroup. 2000 Mathematics Subject Classification. 12E05, 16S50