Permutation polynomials of the form L(x)+S2ka+S2kb over Fq3kFq3k

Let q be a power of 2, k   a positive integer and let Sk=x+xq+⋯+xqk−1∈Fq[x]Sk=x+xq+⋯+xqk−1∈Fq[x]. In this paper, we present a number of classes of explicit permutation polynomials on Fq3kFq3k, which are of the form L(x)+S2ka+S2kb, where a∈{1,qk,q2k}a∈{1,qk,q2k}, b∉{1,qk,q2k}b∉{1,qk,q2k}, and L(x)L(x) are linearized polynomials. We also point out an application of these permutation polynomials in combinatorics, cryptography and sequences.