Optimal normal bases
Purchase on Springer.com
$39.95 / €34.95 / £29.95*
Rent the article at a discountRent now
* Final gross prices may vary according to local VAT.
Let K ⊂ L be a finite Galois extension of fields, of degree n. Let G be the Galois group, and let (<α)<∈G be a normal basis for L over K. An argument due to Mullin, Onyszchuk, Vanstone and Wilson (Discrete Appl. Math. 22 (1988/89), 149–161) shows that the matrix that describes the map x → αx on this basis has at least 2n - 1 nonzero entries. If it contains exactly 2n - 1 nonzero entries, then the normal basis is said to be optimal. In the present paper we determine all optimal normal bases. In the case that K is finite our result confirms a conjecture that was made by Mullin et al. on the basis of a computer search.
- R.C. Mullin, A characterization of th extremal distributions of optimal normal bases, Proc. Marshall Hall Memorial Conference, Burlington, Vermont, 1990, to appear.
- R.C. Mullin, I.M. Onyszchuk, S.A. Vanstone, and R.M. Wilson, Optimal normal bases in GF(pn), Discrete Appl. Math. Vol. 22 (1988/89), pp. 149–161.
- Optimal normal bases
Designs, Codes and Cryptography
Volume 2, Issue 4 , pp 315-323
- Cover Date
- Print ISSN
- Online ISSN
- Kluwer Academic Publishers
- Additional Links
- Industry Sectors