00000cab a22000003a 4500 UP-99796217608517743 Buklod 20231007234513.0 m |o d | ta 080912s xx d | ||r ||||| || (iLib)UPD-00051795511 DENGII eng Dobbertin, Hans One-to-One Highly Nonlinear Power Functions on GF(2n). Vol. 9, no. 2 pp. 139-152 It is an important problem to determine all one-to-one power functions on GF(2n) possessing a maximal nonlinearity. Unfortunately the maximal nonlinearity is not known explicitly for even n. But there is a very reasonable conjecture for it. Assuming that this conjecture is actually true we give an overview about all known cases and add two new results for even n. We expect that now all one-to-one power functions with maximal nonlinearity are found, with exception of conjectures of Welch and Niho for odd n. Boolean functions. Power functions. Walsh transform. Maximal nonlinearity. Crosscorrelation of binary m -sequences. Weight distribution of cyclic codes. Applicable algebra in engineering, communication and computing. 9, 2 (1998). FO UPD DENG-II Article