Curves related to Coulter's maximal curves

Date

2008-01-01

Author

ÇAKÇAK, Emrah
Özbudak, Ferruh

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We study a class of curves over finite fields such that the maximal (respectively minimal) curves of this class form a subclass containing the set of maximal (respectively minimal) curves of Coulter (cf. [R.S. Coulter, The number of rational points of a class of Artin-Schreier curves, Finite Fields Appl. 8 (2002) 397-413, Theorem 8.12]) as a proper subset. We determine the exact number of rational points of the curves in the class and we characterize maximal (respectively minimal) curves of the class as subcovers of some suitable curves. In particular we show that Coulter's maximal curves are Galois subcovers of the appropriate Hermitian curves. (c) 2006 Elsevier Inc. All rights reserved.

Subject Keywords

Theoretical Computer Science, General Engineering, Algebra and Number Theory, Applied Mathematics

URI

https://hdl.handle.net/11511/46133

Journal

FINITE FIELDS AND THEIR APPLICATIONS

DOI

https://doi.org/10.1016/j.ffa.2006.10.003

Collections

Department of Mathematics, Article

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Citation Formats

E. ÇAKÇAK and F. Özbudak, “Curves related to Coulter’s maximal curves,” FINITE FIELDS AND THEIR APPLICATIONS, pp. 209–220, 2008, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/46133.