Self-Complementary Normal Bases in Finite Fields
Abraham Lempel, M.J. Weinberger · SIAM Journal on Discrete Mathematics · 1988
It is shown that $\mathrm{GF} ( q^n )$ has a self complementary normal basis over $\mathrm{GF} ( q )$ if and only if n is odd or $n \equiv 2(\bmod{\text{-}}4)$ and q is even. All existence proofs are constructive and can be readily employed to obtain such bases.