Consider a maximum-length shift-register sequence generated by a primitive polynomial f over a finite field. The set of its subintervals is a linear code whose dual code is formed by all polynomials divisible by f . Since the minimum weight of dual codes is directly related to the strength of the corresponding orthogonal arrays, we can produce orthogonal arrays by studying divisibility of polyn...

Permutation polynomials over finite fields have wide applications in many areas of science and engineering. In this paper, we present six new classes of permutation trinomials over F2n which have explicit forms by determining the solutions of some equations.

Linearized polynomials have attracted a lot of attention because their applications in both geometric and algebraic areas. Let q be prime power, n positive integer σ generator Gal(Fqn:Fq). In this paper we provide closed formulas for the coefficients σ-trinomial f over Fqn which ensure that dimension kernel equals its σ-degree, is linearized with maximum kernel. As consequence, present explicit...

We study the parity of the number of irreducible factors of trinomials over Galois elds of characteristic 2. As a consequence , some suucient conditions for a trinomial being reducible are obtained. For example, x n + ax k + b 2 GF (2 t))x] is reducible if both n; t are even, except possibly when n = 2k, k odd. The case t = 1 was treated by R.G.Swan 10], who showed that x n + x k + 1 is reducib...

Riffaut (2019) conjectured that a singular modulus of degree $h\ge 3$ cannot be root trinomial with rational coefficients. We show this conjecture follows from the GRH, and obtain partial unconditional results.