Gallardo, Luis; Vaserstein, Leonid; Wheland, Ethel Berlekamp’s discriminant and cubic equations in characteristic two. (English) Zbl 1061.11070 JP J. Algebra Number Theory Appl. 3, No. 2, 169-178 (2003). This article investigates the Galois group of extensions \(K/k\) for \(k\) a field of nonzero characteristic. In detail the authors consider \(k\) the function field in one variable over \(F_{2^{2n}}\) and \(K\) obtained by a degree \(3\) polynomial. Their solution is algorithmic and the checking which Galois group occurs can be performed with finitely many steps investigating the coefficients of the polynomial and its Berlekamp discriminant. Reviewer: Tanja Lange (Lyngby) MSC: 11Y16 Number-theoretic algorithms; complexity 11R58 Arithmetic theory of algebraic function fields 11T06 Polynomials over finite fields Keywords:cubic equations; function fields; Galois groups; polynomials PDFBibTeX XMLCite \textit{L. Gallardo} et al., JP J. Algebra Number Theory Appl. 3, No. 2, 169--178 (2003; Zbl 1061.11070)