On permutation polynomials of the formx1+2k+ L(x)
Xin Gong, Guangpu Gao, Wenfen Liu · International Journal of Computer Mathematics · 2015
We investigate the open problem of Li and Wang [On EA-equivalence of certain permutations to power mappings, Des. Codes Cryptogr. 58(2011), pp. 259–269] that whether the polynomial x1+2k+L(x) on GF(2n) is a permutation for gcd(k,n)>1. Several classes of polynomials of the form x1+2k+L(x) are proven to be permutations by decomposing the finite field GF(2n) when n≡0(mod3). Some relationships among this type of permutation polynomials, which allow certain secondary constructions, are also proposed.