On the Equation $x^{2^l+1}+x+a=0$ over $\mathrm{GF}(2^k)$ (Extended Version)


In this paper, the polynomials Pa(x) = x 2l+1 + x + a with a ∈ GF(2) are studied. New criteria for the number of zeros of Pa(x) in GF(2 ) are proved. In particular, a criterion for Pa(x) to have exactly one zero in GF(2 ) when gcd(l, k) = 1 is formulated in terms of the values of permutation polynomials introduced by Dobbertin. We also study the affine… (More)


Figures and Tables

Sorry, we couldn't extract any figures or tables for this paper.