Further results on rational points of the curve y(qn) - y = gamma xqh+1 - alpha over F-qm

Date

2016-06-01

Author

Cosgun, Ayhan
Özbudak, Ferruh
SAYGI, ZÜLFÜKAR

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Let q be a positive power of a prime number. For arbitrary positive integers h, n, m with n dividing m and arbitrary gamma, alpha is an element of F-qm with gamma not equal 0 the number of F-qm - rational points of the curve y(qn) - y = gamma x(qh+1) - alpha is determined in many cases (Ozbudak and Saygi, in: Larcher et al. (eds.) Applied algebra and number theory, 2014) with odd q. In this paper we complete some of the remaining cases for odd q and we also present analogous results for even q.

Subject Keywords

Finite fields, Algebraic curves, Rational points, Artin-Schreier type curve

URI

https://hdl.handle.net/11511/47008

Journal

DESIGNS CODES AND CRYPTOGRAPHY

DOI

https://doi.org/10.1007/s10623-015-0107-1

Collections

Department of Mathematics, Article

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Citation Formats

A. Cosgun, F. Özbudak, and Z. SAYGI, “Further results on rational points of the curve y(qn) - y = gamma xqh+1 - alpha over F-qm,” DESIGNS CODES AND CRYPTOGRAPHY, pp. 423–441, 2016, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/47008.