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

This paper proposes a useful method for constructing a self-dual normal basis in an arbitrary extension field F_pm 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) 2 k m + 1 is a prime number, (2a) the order of p in F_{2 k m + 1} is 2 k m, (2b) 2 {does not divide} k m 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_pm.