New Construction of Optimal Type-II Binary Z-Complementary Pairs

New Construction of Z-Optimal Type-II Even-Length Quadriphase Z-Complementary Pairs

“…Furthermore, when a Z-optimal or an optimal Type-II OL-BZCP or EL-BZCP is employed, the output of this construction is Z-optimal. Incidentally, the aforementioned conclusion has been mathematically proved by [4]. Via a computer searching, two optimal Type-II BZCPs…”

“…In contrast to Type-II BZCPs, Type-II QZCPs have their own special advantages. Type-II OL-QZCPs have larger width of ZCZ than Type-II OL-BZCPs of the same length N , due to the fact that the largest width of ZCZ in the latter is (N + 1)/2 [1], [4], [6]. Type-II EL-QZCPs have smaller OSPAS than Type-II EL-BZCPs of the same length, due to that OSPAS in the latter is 4 [4].…”

“…After calculation, the sums of these two pairs are (10, −2j, 0, 0, 0) 4 τ =0 and (12, 2j, 0, 0, 0, 0) 5 τ =0 , respectively. In fact, the conclusion on OSPAS 2 in Type-II QZCPs has been verified in a mathematical derivation in [5].…”

“…No matter Type-II EL-BZCPs or Type-II EL-QZCPs, optimal and Z-optimal systematic constructions of such pairs are challenging (please see [4] for the concepts of optimal and Z-optimal Type-II EL-BZCPs). To date, only a systematic construction of Z-optimal Type-II EL-BZCPs of lengths in the form of 3 × 2 α 10 β 26 γ * * and 14 × 2 α 10 β 26 γ has been presented [4]. By making use of conversion construction from BZCPs to QZCPs in [7], the resultant pairs from [4] can be transformed into Z-optimal Type-II EL-QZCPs with the unaltered lengths.…”

“…To date, only a systematic construction of Z-optimal Type-II EL-BZCPs of lengths in the form of 3 × 2 α 10 β 26 γ * * and 14 × 2 α 10 β 26 γ has been presented [4]. By making use of conversion construction from BZCPs to QZCPs in [7], the resultant pairs from [4] can be transformed into Z-optimal Type-II EL-QZCPs with the unaltered lengths. No systematic constructions for producing optimal Type-II EL-BZCPs and EL-QZCPS exist currently.…”