Abstract
In this paper, we prove the following results: 1) A normal basis N over a finite field is equivalent to its dual basis if and only if the multiplication table of N is symmetric; 2) The normal basis N is self–dual if and only if its multiplication table is symmetric and Tr(α2) = 1, where α generates N; 3) An optimal normal basis N is self–dual if and only if N is a type–I optimal normal basis with q = n = 2 or N is a type–II optimal normal basis.
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This work is supported by NSFC, Grant No. 10128103
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Liao, Q.Y., Sun, Q. Normal Bases and Their Dual–Bases over Finite Fields. Acta Math Sinica 22, 845–848 (2006). https://doi.org/10.1007/s10114-005-0613-6
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DOI: https://doi.org/10.1007/s10114-005-0613-6