A Direct Construction of Inter-Group Complementary Code Set

Complete complementary codes (CCCs) is a collection of mutually orthogonal complementary codes and Inter-group complementary (IGC) code set consists of multiple disjoint groups of 2-D codes. IGC code set has large set size than CCC and both can be applicable in multicarrier code-division multiple access. The aperiodic autocorrelation function sidelobes of any IGC code is zero for all time shifts inside the zero-correlation zone (ZCZ). The aperiodic crosscorrelation functions (ACCF) of any two distinct IGC codes are zero everywhere if they are from two different groups; when they are drawn from the same group, their ACCFs are zero inside the ZCZ width. This paper presents a direct construction of the IGC code set, which can support interference-free code-division multiplexing using second-order generalized Boolean functions. We relate our construction with a graph where the ZCZ width depends on the number of isolated vertices presented in a graph after the deletion of some vertices. Moreover, our construction is capable of generating the IGC code set with more flexible parameters.