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Factorization and irreducibility of composed products
Lukas Kölsch, Lucas Krompholz, Gohar M. Kyureghyan
Brawley and Carlitz introduced diamond products of elements of finite fields and associated composed products of polynomials in 1987. Composed products yield a method to construct…
Constructing irreducible polynomials recursively with a reverse composition method
Anna-Maurin Graner, Gohar M. Kyureghyan
We suggest a construction of the minimal polynomial of over from the minimal polynomial for all positive integers whos…
A recurrent construction of irreducible polynomials of fixed degree over finite fields
Gohar M. Kyureghyan, Melsik K. Kyureghyan
In this paper we consider in detail the composition of an irreducible polynomial with X^2 and suggest a recurrent construction of irreducible polynomials of fixed degree over finit…
Permutation polynomials of the form x+c*Tr(x^k)
Gohar Kyureghyan, Michael Zieve
Let F_{q^n} be the field of order q^n, and let Tr be the trace map from F_{q^n} to its q-element subfield. We exhibit nine sequences of polynomials of the form f(x):=x+c*Tr(x^k), w…
On Inversion in Z_{2^n-1}
Gohar M. Kyureghyan, Valentin Suder
In this paper we determined explicitly the multiplicative inverses of the Dobbertin and Welch APN exponents in Z_{2^n-1}, and we described the binary weights of the inverses of the…
Constructing permutations of finite fields via linear translators
Gohar M. Kyureghyan
We describe several families of permutation polynomials obtained using functions with linear translators.