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Finding normal bases over finite fields with prescribed trace self-orthogonal relations
[article]
2013
arXiv
pre-print
Normal bases and self-dual normal bases over finite fields have been found to be very useful in many fast arithmetic computations. It is well-known that there exists a self-dual normal basis of F_2^n over F_2 if and only if 4∤ n. In this paper, we prove there exists a normal element α of F_2^n over F_2 corresponding to a prescribed vector a=(a_0,a_1,...,a_n-1)∈F_2^n such that a_i=Tr_2^n|2(α^1+2^i) for 0≤ i≤ n-1, where n is a 2-power or odd, if and only if the given vector a is symmetric
arXiv:1303.2283v1
fatcat:4kh5b2pwjnd23jeqtl53mu5mey