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Berlekamp’s discriminant and cubic equations in characteristic two. (English) Zbl 1061.11070

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.

MSC:

11Y16 Number-theoretic algorithms; complexity
11R58 Arithmetic theory of algebraic function fields
11T06 Polynomials over finite fields
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