Based on a computer search, Anne Canteaut conjectured that the exponent 22r +2r + 1 in F26r and the exponent (2r + 1)2 in F24r yield bent monomial functions. These conjectures are proved in [A. Canteaut, P. Charpin, and G. Kyureghyan, A new class of monomial bent functions, in Proceedings of the 2006 IEEE International Symposium on Information Theory, (ISIT 06 Seattle), IEEE Press, Piscataway, NJ, 2006, pp. 903
Pascale Charpin, Gohar M. M. Kyureghyan