A new class of permutation quadrinomial over 𝔽q2 with characteristic 5

Let [Formula: see text], [Formula: see text] be a natural number, [Formula: see text] the finite field of order [Formula: see text], and [Formula: see text]. In this paper, we find that the quadrinomial [Formula: see text] is a permutation polynomial if [Formula: see text] is a positive integer for [Formula: see text]; [Formula: see text] is odd for [Formula: see text] and [Formula: see text] is even for [Formula: see text]. We also find that [Formula: see text] is a permutation quadrinomial over [Formula: see text].