Construction of spectrally-null-constrained zero-correlation zone sequences with flexible support

In recent years, zero-correlation zone (ZCZ) sequences have been studied due to their significant applications in quasi-synchronous code division multiple access (QS-CDMA) systems and other wireless communication domains. However, in a cognitive radio (CR) network, it is desirable to design ZCZ sequences having spectrally-null-constrained (SNC) property to achieve a low spectral density profile. This paper focuses on the construction of SNC-ZCZ sequences having flexible support, where support refers to a collection of indices corresponding to non-zero entries in the sequence. The proposed SNC-ZCZ sequences are reduced to traditional ZCZ sequences when the support size is equal to the length of the sequence. To obtain ZCZ sequences, we first propose a construction of traditional/SNC-complete complementary codes (SNC-CCCs) using a class of extended Boolean functions (EBFs). With the help of this class, we propose another class of EBFs that generates asymptotically optimal traditional/SNC-ZCZ sequences of prime-power lengths with respect to Tang-Fan-Matsufuzi bound. Furthermore, a relation between the second-order cosets of first-order generalized Reed-Muller (GRM) code and the proposed traditional ZCZ sequences is also established. The enumeration of traditional ZCZ sequences within a GRM code is also established. This enumeration is achieved by tallying the distinct second-order cosets of the first-order GRM code and quantifying the number of ZCZ sequences residing within a particular coset. Moreover, the Hamming distance of the proposed traditional ZCZ sequences is also computed.