Two Indicators of Cross-Correlation for the Functions from Zqn to Z2q

Abstract

Boolean functions play an important role in the design of secure cryptosystems and code division multiple access (CDMA) communication. Several possible generalizations of Boolean functions have been obtained in recent years. In this paper, we analyze the properties of functions from Z_qⁿ to Z_2q in terms of their Walsh-Hadamard transform (WHT). We provide a relationship between cross-correlation and the WHT of these functions. Also, we present a necessary and sufficient condition for the functions to have complementary autocorrelation. The Parseval’s identity for the current setup of these functions is obtained. Further, we obtained the modulus indicator (MI) and the sum-ofsquares-modulus indicator (SSMI) of cross-correlation among two functions for the current setup.