turkmath.org

Modified planar functions are introduced to describe (2^n,2^n,2^n,1) relative difference sets (RDS) R as a graph of a function on the finite field F_2n. These are analogs of planar functions in odd characteristic q to describe (q^n, q^n, q^n, 1) RDSs. We point out that the projections of R are (2^n, 2, 2^n, 2^{n−1}) RDS that can be described by bent_4 functions, and we investigate the equivalence of their relative difference sets. In particular, we show that two extended affine equivalent bent functions may give rise to bent_4 functions whose corresponding RDSs are inequivalent.