Some new forms of permutation polynomials over finite fields with even characteristic
Abstract
Let q=2m. In this paper, we propose several classes of permutation polynomials of the forms L1(xd1)k1+L2(xd2)k2, L1(xd1)k1+L3(xd2+xd3)k2 over Fq2 and L1(xd1)+L3(c1xd2+c2xd3) over Fq3 from certain linearized polynomials L1(x)=x+a0xq,L2(x)=b0x+b1xq,L3(x)=x+xq. The numerical results suggest that the sufficient conditions we find in the first class of permutation polynomials (see Theorem 3.2) are also necessary. Some known results on permutation polynomials over Fq2 are covered by ours.
Fields of Study & Subjects
Coding theory and cryptography
Advanced Combinatorial Mathematics
Algebraic Geometry and Number Theory
Publication details
- Journal / source
- Communications in Algebra
- Pages
- 1–21
- Publication date
- 22 February 2026
- Language
- EN