Normal bases via general Gauss periods |
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| Authors: | Sandra Feisel Joachim von zur Gathen M. Amin Shokrollahi. |
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| Affiliation: | Fachbereich 17 Mathematik-Informatik, Universität-GH Paderborn, D-33095 Paderborn, Germany ; Fachbereich 17 Mathematik-Informatik, Universität-GH Paderborn, D-33095 Paderborn, Germany ; International Computer Science Institute, 1947 Center Street, Berkeley, CA 94704-1198, USA |
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| Abstract: | Gauss periods have been used successfully as a tool for constructing normal bases in finite fields. Starting from a primitive  th root of unity, one obtains under certain conditions a normal basis for  over  , where  is a prime and  for some integer  . We generalize this construction by allowing arbitrary integers  with  , and find in many cases smaller values of  than is possible with the previously known approach. |
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