A survey on p-ary and generalized bent functions

Official URL: https://dx.doi.org/10.1007/s12095-022-00570-x

Boolean bent functions have been introduced by Rothaus in 1966, bent functions in odd characteristic were first considered in 1985 by Kumar, Scholtz, and Welch. Two books on bent functions and some surveys on bent functions and related topics mainly deal with the Boolean case. In this survey, we focus on bent and vectorial bent functions in odd characteristic. Lately, one can observe increasing interest in the bentness of functions from elementary abelian into cyclic groups. Following this development, we also survey recent results on this class of functions.