Permutation polynomials of index q + 1 over F q 2
Xiutao Feng, Qiang Wang · Finite Fields and Their Applications · 2026
We provide a generic construction of permutation polynomials over F q 2 with index q + 1 from any permutation polynomial of F q . We also extend our construction using polynomials with coefficients in F q 2 such that they are injective over a subset of F q 2 ⁎ , which corresponds to the set μ q + 1 of all ( q + 1 ) -th roots of unity.