Geodesic
Generic polynomials for transitive subgroups of the group $S_4$ over fields of characteristic 2
Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 13, Tome 330 (2006), pp. 247-258 Cet article a éte moissonné depuis la source Math-Net.Ru

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Generic polynomials for the symmetric group $S_4$, the Klein group $V_4$, the cyclic group of order 4, the dihedral group $D_4$ and the alternative group $A_4$ over fields of characteristic 2 are explicitly described. 
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A. È. Sergeev; A. V. Yakovlev. Generic polynomials for transitive subgroups of the group $S_4$ over fields of characteristic 2. Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 13, Tome 330 (2006), pp. 247-258. http://geodesic.mathdoc.fr/item/ZNSL_2006_330_a13/

[1] E. Witt, “Konstruktion von galoisschen Körpern der Charakteristik $p$ zu vorgegebener Gruppe der Ordnung $p^f$”, J. Reine Angew. Math., 174 (1936), 237–245 | DOI

[2] G. Kemper, E. Mattig, “Generic polynomials with few parameters”, Symb. Comp., 30 (2000), 843–857 | DOI | MR | Zbl

[3] G. Kemper, Das Noethersche Problem und generische Polynome, Dissertation, Universitat Heidelberg, 1994

[4] H. Tsunogai, K. Hashimoto, “Generic polynomials over $\mathbb{Q}$ with two parameters for the transitive groups of degree five”, Proc. Japan Acad. Ser. A Math. Sci., 79 (2003), 142–145 | DOI | MR | Zbl

[5] J.-P. Serre, Topics in Galois theory, Jones and Barthelett Publ., Boston, 1992 | MR | Zbl