A general construction of permutation polynomials of Fq2

Let r be a positive integer, h(X)∈Fqjavax.xml.bind.JAXBElement@3085cc0e[X], and μq+1 be the subgroup of order q+1 of Fqjavax.xml.bind.JAXBElement@1830d635⁎. It is well known that Xrh(Xq−1) permutes Fqjavax.xml.bind.JAXBElement@70a82a15 if and only if gcd(r,q−1)=1 and Xrh(X)q−1 permutes μq+1. There are many ad hoc constructions of permutation polynomials of Fqjavax.xml.bind.JAXBElement@73c82905 of this type such that h(X)q−1 induces monomial functions on the cosets of a subgroup of μq+1. We give a general construction that can generate, through an algorithm, all permutation polynomials of Fqjavax.xml.bind.JAXBElement@6db36ece with this property, including many which are not known previously. The construction is illustrated explicitly for permutation binomials and trinomials.