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Citation - WoS: 1
Citation - Scopus: 1
The Number of Irreducible Polynomials Over Finite Fields With Vanishing Trace and Reciprocal Trace
(Springer, 2022) Cakiroglu, Yagmur; Yayla, Oguz; Yilmaz, Emrah Sercan
We present the formula for the number of monic irreducible polynomials of degree n over the finite field F-q where the coefficients of x(n)(-1) and x vanish for n >= 3. In particular, we give a relation between rational points of algebraic curves over finite fields and the number of elements a is an element of F-qn for which Trace(a) = 0 and Trace(a(-1)) = 0.
Citation - WoS: 13
Citation - Scopus: 12
Classification of Permutation Polynomials of the Form x^{3< of F_{q2< Where g(x< = x^{3< + bx Plus c and b, c ∈ F_q<}}}
(Springer, 2022) Ozbudak, Ferruh; Temur, Burcu Gulmez
We classify all permutation polynomials of the form x(3) g(x(q-1)) of F-q2 where g(x) = x(3) + bx + c and b, c is an element of F-q*. Moreover we find new examples of permutation polynomials and we correct some contradictory statements in the recent literature. We assume that gcd(3, q -1) = 1 and we use a well known criterion due to Wan and Lidl, Park and Lee, Akbary and Wang, Wang, and Zieve.