Partial spreads and hyperbent functions in odd characteristic

We study bent functions which are as different as possible from linear functions. Functions that remain bent under all bijective monomial substitutions are called hyperbent. In Chapter 2 we introduce partial spreads to construct a family of bent functions on vector spaces of even dimension over a finite field. This generalizes the construction given by Dillon for fields of characteristic 2. In Chapter 3 we use finite fields to introduce an explicit family of functions in the trace form whose hyperbentness can be tested using results of Chapter 2. This test is more efficient than using the definition of a bent function. It is an analogue of a result by Charpin and Gong for characteristic 2. The motivation for studying bent functions is their important role in cryptography and coding theory. For example, the CAST cipher constructed using bent functions is approved for use by the Canadian government.