Primitive normal polynomials with the last half coefficients prescribed (Q623240)

The author proves that for any given \(n\geq 2\) there exists a constant \(c(n)\) such that for any prime power \(q>c(n)\) there exists a primitive normal polynomial of degree \(n\) over \(\mathbb F_q\) with the last \(\lfloor n/2\rfloor\) coefficients prescribed and the last coefficient is a primitive element of \(\mathbb F_q\). If the prescribed coefficients are \((0,\dots,0,b)\) and \(n\) is odd, one more coefficient can be prescribed. This complements and partly improves the results of \textit{S. Q. Fan, W. B. Han} and \textit{K. Q. Feng} [``Primitive normal polynomials with multiple coefficients prescribed: an asymptotic result'', Finite Fields Appl. 13, No. 4, 1029--1044 (2007; Zbl 1132.11054)].