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An elementary proof and an extension of Thas' theorem on k-arcs

Published online by Cambridge University Press:  04 October 2011

Hitoshi Kaneta  and
Tatsuya Maruta
Hitoshi Kaneta
Affiliation:
Department of Mathematics, Okayama University, Okayama 700, Japan
Tatsuya Maruta
Affiliation:
Department of Mathematics, Okayama University, Okayama 700, Japan
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Extract

Let q be the finite field of q elements. Denote by Sr q the projective space of dimension r over q. In Sr,q, where r ≥ 2, a k-arc is defined (see [4]) as a set of k points such that no j + 2 lie in a Sj,q, for j = 1,2,…, r−1. (For a k-arc with k > r, this last condition holds for all j when it holds for j = r−1.) A rational curve Cn of order n in Sr,q, is the set

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 105 , Issue 3 , May 1989 , pp. 459 - 462
Copyright
Copyright © Cambridge Philosophical Society 1989

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References

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