Some new results on permutation trinomials over finite fields with even characteristic

Kirpa Garg, Sartaj Ul Hasan, Chandan Kumar Vishwakarma

The construction of permutation trinomials of the form $X^r(X^{\hat{I}\pm (2^m-1)}+X^{{\hat{I}}^2(2^m-1)}+1)$ over $\F_{2^{2m}}$, where $m,r\text{ and }\hat{I}\pm >{\hat{I}}^2$ are positive integers, is an active…