Partial spread and vectorial generalized bent functions

In this paper we generalize the partial spread class and completely describe it for generalized Boolean functions from F 2 to Z2t . Explicitly, we describe gbent functions from F 2 to Z2t , which can be seen as a gbent version of Dillon’s PSap class. For the first time, we also introduce the concept of a vectorial gbent function from F 2 to Zmq , and determine the maximal value which m can attain for the case q = 2. Finally we point to a relation between vectorial gbent functions and relative difference sets.