Curves over finite fields and permutations of the form x(k) - gamma Tr(x)
Anbar Meidl, Nurdagül (2019) Curves over finite fields and permutations of the form x(k) - gamma Tr(x). Turkish Journal of Mathematics, 43 (1). pp. 533-538. ISSN 1300-0098 (Print) 1303-6149 (Online)
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Official URL: http://dx.doi.org/10.3906/mat-1811-27
We consider the polynomials of the form P(x) = x(k) - gamma Tr(x) over F-qn for n >= 2. We show that P(x) is not a permutation of F-qn in the case gcd(k,q(n) - 1) > 1. Our proof uses an absolutely irreducible curve over( )F(qn) and the number of rational points on it.
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