Correlation of Multiple Bent Function Signal Sets

Abstract

Observing a phenomenon that the pre-image set of nonzero Hadamard spectra of the composition of a function and a trace function is independent of the function, a construction of multiple bent function signal sets using different bent functions is given. Their correlation and high-order shift-distinct property are discussed. As a by-product, the union of the multiple bent function signal sets produces a signal set with low correlation zone and much larger size of the other known constructions.