A recursive construction of p-ary bent functions which are not weakly regular

In this paper, we introduce a recursive construction of p-ary bent functions, where p is an odd prime. Several new non-quadratic bent functions over fields with characteristic 5, 7, 11, 13, 17, 19, 23 are found by computer search, all of which are homogeneous. A ternary bent function whose algebraic degree attains the upper bound is given. So far it is the only known example with this property.