Geodesic
On normal bases of a finite field
Sbornik. Mathematics, Tome 61 (1988) no. 2, pp. 485-494 Cet article a éte moissonné depuis la source Math-Net.Ru

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In this paper irreducible polynomials $f(x)$ of degree $t$ are constructed over a finite field of characteristic $p>0$ with linearly independent roots, where the integer $t$ divides one of the numbers $p$, $q-1$, or $q+1$. Properties of normal bases of the field $F_{q^t}$ over $F_q$ formed by the roots $\{\omega_1,\dots,\omega_t\}$ of $f(x)$ are also studied. In particular, it is shown that the “multiplication table” of such a basis has the form $\omega_i\omega_j=\alpha_{i-j}\omega_i+\alpha_{j-1}\omega_j+\gamma$, $i\ne j$, $\alpha_k$, $\gamma\in F_q$. Bibliography: 3 titles. 
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     author = {V. M. Sidel'nikov},
     title = {On normal bases of a~finite field},
     journal = {Sbornik. Mathematics},
     pages = {485--494},
     year = {1988},
     volume = {61},
     number = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1988_61_2_a13/}
}
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V. M. Sidel'nikov. On normal bases of a finite field. Sbornik. Mathematics, Tome 61 (1988) no. 2, pp. 485-494. http://geodesic.mathdoc.fr/item/SM_1988_61_2_a13/

[1] Huppert B., Endliche gruppen. 1, Springer, N.Y., 1967 | MR | Zbl

[2] Busarkin V. M., Gorchakov Yu. M., Konechnye rasscheplyaemye gruppy, Nauka, M., 1968 | MR

[3] Ore O., “Contributions to the theory of finite fields”, Trans. Amer. Math. Soc., 36:2 (1934), 243–275 | DOI | MR