A method for constructing a self-dual normal basis in odd characteristic extension fields

Authors:
Yasuyuki Nogami;Hiroaki Nasu;Yoshitaka Morikawa;Satoshi Uehara
Affiliations:
Faculty of Engineering, Okayama University, Okayama-shi 700-8530, Japan;Faculty of Engineering, Okayama University, Okayama-shi 700-8530, Japan;Faculty of Engineering, Okayama University, Okayama-shi 700-8530, Japan;Department of Information and Media Engineering, The University of Kitakyushu, Kitakyushu-shi 808-0135, Japan
Venue:
Finite Fields and Their Applications
Year:
2008

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Abstract

This paper proposes a useful method for constructing a self-dual normal basis in an arbitrary extension field F"p"^"m such that 4p does not divide m(p-1) and m is odd. In detail, when the characteristic p and extension degree m satisfies the following conditions (1) and either (2a) or (2b); (1) 2km+1 is a prime number, (2a) the order of p in F"2"k"m"+"1 is 2km, (2b) 2@?km and the order of p in F"2"k"m"+"1 is km, we can consider a class of Gauss period normal bases. Using this Gauss period normal basis, this paper shows a method to construct a self-dual normal basis in the extension field F"p"^"m.