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

Cosgun A., ÖZBUDAK F., SAYGI Z.

DESIGNS CODES AND CRYPTOGRAPHY, vol.79, no.3, pp.423-441, 2016 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 79 Issue: 3
  • Publication Date: 2016
  • Doi Number: 10.1007/s10623-015-0107-1
  • Journal Name: DESIGNS CODES AND CRYPTOGRAPHY
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.423-441
  • Middle East Technical University Affiliated: Yes

Abstract

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.