ON THE CURVE Y n = X m + X OVER FINITE FIELDS
نویسندگان
چکیده
We show that a maximal curve over Fq2 defined by the affine equation y = f(x), where f(x) ∈ Fq2 [x] has degree coprime to n, is such that n is a divisor of q+1 if and only if f(x) has a root in Fq2 . In this case, all the roots of f(x) belong to Fq2 ; cf. Thm. 1.2, Thm. 4.3 in [J. Pure Appl. Algebra 212 (2008), 2513–2521]. In particular, we characterize certain maximal curves defined by equations of type y = x + x over finite fields.
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