Normal Bases via General Gauss Periods

TitleNormal Bases via General Gauss Periods
Publication TypeTechnical Report
Year of Publication1997
AuthorsGathen, J. von zur, Schlink S., & M. Shokrollahi A.
Other Numbers1086
Keywordsalgebraic number theory, cyclotomic fields, Finite Fields, Gauss periods, normal bases

Gauss periods have been used successfully as a tool for constructing normal bases in finite fields. Starting from a primitive rth root of unity, one obtains under certain conditions a normal basis for F_qn over F_q, where r is a prime and nk = r - 1 for some integer k. We generalize this construction by allowing arbitrary integers r with nk = ?(r), and find in many cases smaller values of k than is possible with the previously known approach.

Bibliographic Notes

ICSI Technical Report TR-97-020

Abbreviated Authors

J. von zur Gathen, S. Schlink, and M. A. Shokrollahi

ICSI Publication Type

Technical Report