Publication Details
Title: Normal Bases via General Gauss Periods
Author: J. von zur Gathen, S. Schlink, and M. A. Shokrollahi
Group: ICSI Technical Reports
Date: May 1997
PDF: ftp://ftp.icsi.berkeley.edu/pub/techreports/1997/tr-97-020.pdf
Overview:
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 = φ(r), and find in many cases smaller values of k than is possible with the previously known approach. Keywords: Gauss periods, normal bases, finite fields, cyclotomic fields, algebraic number theory
Bibliographic Information:
ICSI Technical Report TR-97-020
Bibliographic Reference:
J. von zur Gathen, S. Schlink, and M. A. Shokrollahi. Normal Bases via General Gauss Periods. ICSI Technical Report TR-97-020, May 1997
Author: J. von zur Gathen, S. Schlink, and M. A. Shokrollahi
Group: ICSI Technical Reports
Date: May 1997
PDF: ftp://ftp.icsi.berkeley.edu/pub/techreports/1997/tr-97-020.pdf
Overview:
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 = φ(r), and find in many cases smaller values of k than is possible with the previously known approach. Keywords: Gauss periods, normal bases, finite fields, cyclotomic fields, algebraic number theory
Bibliographic Information:
ICSI Technical Report TR-97-020
Bibliographic Reference:
J. von zur Gathen, S. Schlink, and M. A. Shokrollahi. Normal Bases via General Gauss Periods. ICSI Technical Report TR-97-020, May 1997