Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8895625 | Finite Fields and Their Applications | 2018 | 19 Pages |
Abstract
Recently, there has been a lot of work on constructions of permutation polynomials of the form (x2m+x+δ)s+x over the finite field F22m, especially in the case when s is of the form s=i(2mâ1)+1 (Niho exponent). In this paper, we further investigate permutation polynomials with this form. Instead of seeking for sporadic construction of the parameter i, we give two general sufficient conditions on i such that (x2m+x+δ)i(2mâ1)+1+x permutes F22m: (i) (2k+1)iâ¡1or2k(mod2m+1); (ii) (2kâ1)iâ¡â1or2k(mod2m+1), where 1â¤kâ¤mâ1 is any integer. It turns out that most of previous constructions of the parameter i are covered by our results, and they yield many new classes of permutation polynomials as well.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Libo Wang, Baofeng Wu,