Abstract
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 on is a permutation for . Several classes of polynomials of the form are proven to be permutations by decomposing the finite field when . Some relationships among this type of permutation polynomials, which allow certain secondary constructions, are also proposed.
Acknowledgements
The authors would like to thank Professor Xiang-Dong Hou for his help in proving the theorems in Section 3.
Disclosure statement
No potential conflict of interest was reported by the authors.