Permutation polynomials (PPs) of the form (x q − x + c) q 2 −1 3 +1 + x over F q 2 were presented by Li, Helleseth and Tang [Finite Fields Appl. 22 (2013) 16-23]. More recently, we have constructed PPs of the form (x q 3, 4, 6 [Finite Fields Appl. 35 (2015) 215-230]. In this paper we concentrate our efforts on the PPs of more general form and d is an arbitrary positive divisor of q 2 − 1. The key step is the construction of a commutative diagram with specific properties, which is the basis of the Akbary-Ghioca-Wang (AGW) criterion. By employing the AGW criterion two times, we reduce the problem of determining whether f (x) permutes F q 2 to that of verifying whether two more polynomials permute two subsets of F q 2 . As a consequence, we find a series of simple conditions for f (x) to be a PP of F q 2 . These results unify and generalize some known classes of PPs.
In REF , authors propose PPs of the form f (x) = (ax q + bx + c) r φ((ax q + bx + c) (q 2 −1)/d ) + ux q + vx over F q 2 .
Large classes of permutation polynomials over F q 2 .
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