On the boomerang uniformity of a class of permutation quadrinomials over finite fields

Let F-2n be a finite field with 2n elements and f(subset of)(x) = c(0)x(2m(2k+1)) + c(1)x(2m+k+1) + c(2)x(2m+2k) + c(3)x(2k+1) & ISIN; F-2n [x], where n, m and k are positive integers with n = 2m and gcd(m, k) = e. In this paper, motivated by a recent work of Li, Xiong and Zeng (Li et al. (2021) [12]), we further study the boomerang uniformity of f(subset of)(x) by using similar ideas and carrying out particular techniques in solving equations over finite fields. As a consequence, we general-ize Li, Xiong and Zeng's result from the case of m being odd and e =1 to that of both m/e and k/e being odd. (c) 2022 Elsevier B.V. All rights reserved.