Constructions of Optimal Binary Z-Complementary Sequence Sets With Large Zero Correlation Zone

Construction of Optimal Binary Z-Complementary Code Sets with New Lengths

“…TABLE I compare our works to those presented in [21], [18], [22] and [24]. The construction in [21], [24] generates binary ZCCS of length NPT, but it depends largely on beginning sequences, which increases hardware storage.…”

“…When the equality sign is true, ZCCS is said to be optimal [10]. In the literature, numerous ZCCSs have been proposed by using direct [11]- [18] and indirect [19]- [22] method. In [11]- [14] binary ZCCS of length power-of-two have been presented.…”

“…Sarkar et al in [18] suggested building q-ary ZCCS with a length of the form 2 m + 2 using GBF. In [22], Sun et al proposed a way to build q-ary ZCCS with a length of the form 32 m using GBF. In [21], Das et al proposed q-ary non-power-of-two lengths ZCCS but the construction depends on initial choices of sequences.…”

New Constructions of Mutually Orthogonal Complementary Sets and Z-Complementary Sequence Sets Based on Extended Boolean Functions

“…From Table 2, we see that some constructions of ZCCSs are mainly based on generalized Boolean functions [17][18][19][20][21]. As for other methods, some researchers provided ZCCSs by Zparaunitary (ZPU) matrices [27], GCP, Z-complementary pair (ZCP), unitary matrices [28,29], Pseudo-Boolean functions (PBF) [30,31] and extended Boolean functions [22].…”

“…In order to meet the needs of more practical scenarios, some researchers take up researching optimal ZCCSs. However, most of these optimal ZCCSs based on GBFs have limited lengths [17][18][19][20][21]. To break this limitation, Shen et al raised a new Boolean function and defined it as extended Boolean function (EBF) [22].…”