On constructions of bent, semi-bent and five valued spectrum functions from old bent functions
Sihem Mesnager, Fengrong Zhang · Advances in Mathematics of Communications · 2017
The paper presents methods for designing functions having many applications in particular to construct linear codes with few weights. The former codes have several applications in secret sharing, authentication codes, association schemes and strongly regular graphs. We firstly provide new secondary constructions of bent functions generalizing the well-known Rothaus' constructions as well as their dual functions. From our generalization, we show that we are able to compute the dual function of a bent function built from Rothaus' construction. Next we present a result leading to a new method for constructing semi-bent functions and few Walsh transform values functions built from bent functions.