New classes of permutation trinomials of [formula omitted].

In recent years, there have been a lot of research towards finding conditions under which the trinomial x r (x α (q − 1) + x β (q − 1) + 1) permutes F 2 2 m with α > β and r being positive integers. The authors of [6,10,24] have determined these conditions when α ≤ 5 for certain values of β and r. In this paper, we work for α = 6 and determine four new classes of such permutation trinomials. Our contribution encompasses the investigation of these unexplored classes. Additionally, we analyze their quasi-multiplicative equivalence with already known permutation trinomials for m ≥ 1. Through our research, we demonstrate that two of these determined classes are new, and for others, we explicitly compute the exponent for which they become equivalent. [ABSTRACT FROM AUTHOR]