Interest in normal bases over finite fields stems from both purely mathematical curiosity and practical applications. The practical aspects of normal bases will be treated in Chapter 5. In the present chapter, we discuss the theoretical aspects of normal bases over finite fields.
KeywordsFinite Field Characteristic Polynomial Null Space Normal Basis Minimal Polynomial
Unable to display preview. Download preview PDF.
- E. Artin, Galois Theory, University of Notre Dame Press, South Bend, Ind., 1966.Google Scholar
- E. Bach, J. Driscoll and J. Shallit, “Factor refinement”, Proceedings of the First Annual Acm-SIAM Symposium on Discrete Algorithms (1990), 202–211 (full version to appear in J. of Algorithms). Google Scholar
- I. Blake, S. Gao and R. Mullin, “On normal bases in finite fields”, preprint, 1992.Google Scholar
- I. Blake, S. Gao and R. Mullin, “Factorization of cx q+1 + dax q -ax- b and normal bases over GF(q)”, Research Report Corr 91–26, Faculty of Mathematics, University of Waterloo, 1991.Google Scholar
- S. Gao, Normal Bases over Finite Fields, Ph.D. thesis, Department of Combinatorics and Optimization, University of Waterloo, in preparation.Google Scholar
- D. Jungnickel, “Trace-orthogonal normal bases”, Discrete Applied Math., to appear.Google Scholar
- R. Lidl and H. Niederreiter, Finite Fields, Cambridge University Press, 1987.Google Scholar
- S. Schwarz, “Construction of normal bases in cyclic extensions of a field”, Czechslovak Math. J., 38 (1988), 291–312.Google Scholar
- M. Wang, I. Blake and V. Bhargava, “Normal bases and irreducible polynomials in the finite field Gf(22r)”, preprint, 1990.Google Scholar