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On Conics Over a Finite Field

Published online by Cambridge University Press:  20 November 2018

Fuanglada R. Jung
Fuanglada R. Jung*
Affiliation:
Kansas State University, Manhattan y Kansas; Chulalongkorn University, Bangkok y Thailand
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Let F denote a Galois field of order q and odd characteristic p, and F* = F\{0}. Let Sn denote an n-dimensional affine space with base field F. E. Cohen [1] had proved that if n ≧ 4, there is no hyperplane of Sn contained in the complement of the quadric Qn of Sn defined by

1.1

and in S3, there are q + 1 or 0 planes contained in the complement of Q3 according as — aα is not or is a square of F.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 26 , Issue 6 , December 1974 , pp. 1281 - 1288
Copyright
Copyright © Canadian Mathematical Society 1974

References

1. Cohen, E., Linear and quadratic equations in a Galois field with applications to geometry, Duke Math. J. 32 (1965), 633–641.Google Scholar
2. Dickson, L. E., Linear group, with an exposition of the Galois field theory, (Lipezig, 1901: reprinted by Dover, 1958).Google Scholar
3. Jung, F. R., Ph.D. thesis, Kansas State University, 1969.Google Scholar