On some permutation binomials and trinomials over F2n
Designs, Codes, and Cryptography
In this work, we completely characterize (1) permutation binomials of the form x2n-12t-1+1+ax∈F2n[x],n=2st,a∈F22t∗, and (2) permutation trinomials of the form x2s+1+x2s-1+1+αx∈F2t[x], where s, t are positive integers. The first result, which was our primary motivation, is a consequence of the second result. The second result may be of independent interest.
Bhattacharya, Srimanta and Sarkar, Sumanta, "On some permutation binomials and trinomials over F2n" (2017). Journal Articles. 2793.