논문KCI 등재
Affine transformation of a normal element and its application
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In this paper, we study affine transformations of normal bases and give an explicit formulation of the multiplication table of an affine transformation of a normal basis. We then discuss constructions of self-dual normal bases using affine transformations of traces of a type I optimal normal basis and of a Gauss period normal basis.
Abstract
In this paper, we study affine transformations of normal bases and give an explicit formulation of the multiplication table of an affine transformation of a normal basis. We then discuss constructions of self-dual normal bases using affine transformations of traces of a type I optimal normal basis and of a Gauss period normal basis.
참고문헌 (8)
- M. Christopoulou, "The trace of an optimal normal element and low complexity normal bases", Des. Codes Cryptogr, 49, pp.199~215 (2008)
- M. Christopoulou, "Gauss periods as constructions of low complexity normal bases", Des. Codes Cryptogr, 62, pp.43~62 (2012)
- S. Gao, "Normal bases over finite fields", PhD, pp.1993
- D. Jungnickel, "Trace-orthogonal normal bases", Discrete Applied Mathematics, 47, pp.233~249 (1993)
- A. Lempel, "Self-complementary normal bases in finite fields", SIAM J. Discrete Math, 1, pp.758~767 (1988)
- Q. Liao, "The Gaussian normal basis and its trace basis over finite fields", J. Number Theory, 132, pp.1507~1518 (2012)
- R.C Mullin, "Optimal normal bases in GF(pnpn)", Discrete Appl. Math, 22, pp.149~161 (1989)
- Y. Nogami, "A method for constructing a self-dual normal basis in odd characteristic extension fields", Finite Fields Appl, 14, pp.867~876 (2008)
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