3 research outputs found
New Sets of Optimal Odd-length Binary Z-Complementary Pairs
A pair of sequences is called a Z-complementary pair (ZCP) if it has zero
aperiodic autocorrelation sums (AACSs) for time-shifts within a certain region,
called zero correlation zone (ZCZ). Optimal odd-length binary ZCPs (OB-ZCPs)
display closest correlation properties to Golay complementary pairs (GCPs) in
that each OB-ZCP achieves maximum ZCZ of width (N+1)/2 (where N is the sequence
length) and every out-of-zone AACSs reaches the minimum magnitude value, i.e.
2. Till date, systematic constructions of optimal OB-ZCPs exist only for
lengths , where is a positive integer. In this
paper, we construct optimal OB-ZCPs of generic lengths (where are non-negative integers and
) from inserted versions of binary GCPs. The key leading to the
proposed constructions is several newly identified structure properties of
binary GCPs obtained from Turyn's method. This key also allows us to construct
OB-ZCPs with possible ZCZ widths of , and through proper
insertions of GCPs of lengths , respectively. Our proposed OB-ZCPs have applications in
communications and radar (as an alternative to GCPs)
Construction of New Optimal Z-Complementary Code Sets from Z-Paraunitary Matrices
In this paper, we first introduce a novel concept, called Z-paraunitary (ZPU) matrices. These ZPU matrices include conventional PU matrices as a special case. Then, we show that there exists an equivalence between a ZPU matrix and a Z-complementary code set (ZCCS) when the latter is expressed as a matrix with polynomial entries. The proposed ZPU matrix has an advantage over the conventional PU matrix with regard to the availability of wider range of matrix sizes and sequence lengths. In addition, the proposed construction framework can accommodate more choices of ZCCS parameters compared to the existing works