On the number of self-dual bases of $\textrm {GF}(q^ m)$ over $\textrm {GF}(q)$
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- by Dieter Jungnickel, Alfred J. Menezes and Scott A. Vanstone PDF
- Proc. Amer. Math. Soc. 109 (1990), 23-29 Request permission
Abstract:
Let $E = GF({q^m})$ be the $m$-dimensional extension of $F = GF(q)$. We are concerned with the numbers $sd(m,q)$ and $sdn(m,q)$ of self-dual bases and self-dual normal bases of $E$ over $F$, respectively. We completely determine $sd(m,q)$, en route giving a very simple proof for the Sempel-Seroussi theorem which states that $sd(m,q) = 0$ iff $q$ is odd and $m$ is even. Using results of Lempel and Weinberger and MacWilliams, we can also determine $sdn(m,p)$ for primes $p$.References
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Additional Information
- © Copyright 1990 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 109 (1990), 23-29
- MSC: Primary 11T30
- DOI: https://doi.org/10.1090/S0002-9939-1990-1007501-X
- MathSciNet review: 1007501