On the curve y(n) = x(m) + x over finite fields

Author(s)

Tafazolian, Saeed ^[1] ; Torres, Fernando ^[1]

Affiliation

^[1] Univ Estadual Campinas, IMECC, BR-13083859 Campinas, SP - Brazil

• Document type: Journal article
• Source: JOURNAL OF NUMBER THEORY; v. 145, p. 51-66, DEC 2014.
• Web of Science Citations: 9

Abstract

We characterize certain maximal curves over finite fields defined by equations of type y(n) = x(m) + x. Moreover, we show that a maximal curve over F-q2 defined by the affine equation y(n) = f (x), where f (x) is an element of F-q2 {[}x] is separable of degree coprime to n, is such that n is a divisor of q + 1 if and only if f (x) has a root in F-q2. In this case, all the roots of f (x) belong to F-q2; cf. Theorems 1.2 and 4.3 in Garcia and Tafazolian (2008) {[}9]. (C) 2014 Elsevier Inc. All rights reserved. (AU)

• FAPESP's process: 12/02255-3 - CURVES OVER FINITE FIELDS
• Grantee: Saeed Tafazolian
• Support Opportunities: Scholarships in Brazil - Post-Doctoral