Generalized Rothaus construction and non-weakly regular bent functions

In this article a construction of bent functions from an n  -dimensional vector space VnVn over FpFp to FpFp is presented for arbitrary primes p   and dimensions n≥5n≥5. The construction can be seen as generalization of the Rothaus construction for Boolean bent functions. Since vectorial bent functions are used, we recall some classes of vectorial bent functions and employ them to obtain both, weakly regular and non-weakly regular bent functions. The suggested construction provides the second known procedure to design non-weakly regular bent functions.