New constructions of Z-complementary code sets and mutually orthogonal complementary sequence sets

Shen, Bingsheng; Meng, Hua; Yang, Yang; Zhou, Zhengchun

doi:10.1007/s10623-022-01112-5

Cited by 15 publications

(34 citation statements)

References 36 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…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]. However, the parameters of the known direct constructions of ZCCSs based on GBFs are mostly related to 2 and only [22] breaks through this limitation by utilizing the arbitrariness of q.…”

Section: Case 1: Ifmentioning

confidence: 99%

“…But both of these methods only have power of two lengths when q = 2. Other methods for designing MOCSs include PU matrices [20,21], interleaving, Kronecker product [22,23], extended correlation [24] and concatenation [40]. However, These methods are hard to be applied in engineering due to their large space and time requirements in hardware generation.…”

Section: Comparisonmentioning

confidence: 99%

“…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]. Unlike generalized Boolean functions, an extended Boolean function is a mapping from Z m q to Z q , where Z q is the ring of integers modulo q and q is an arbitrary positive integer.…”

Section: Introductionmentioning

confidence: 99%

“…In most previous designs, however, the optimal ZCCSs based on direct methods have limited lengths and the optimal ZCCSs based on indirect methods have limited hardware generations. Recently, Shen et al introduced the concept of EBF and obtained optimal ZCCSs of length q m [40], where q ≥ 2 is a positive integer. This work helps us to construct more optimal ZCCSs.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

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

Xiao

Cao

2022

Preprint

View full text Add to dashboard Cite

Mutually orthogonal complementary sets (MOCSs) have many applications in practical scenarios such as synthetic aperture imaging systems, orthogonal frequency division multiplexing code division multiple access (OFDM-CDMA) systems and multicarrier code division multiple access (MC-CDMA) systems. Z-complementary code sets (ZCCSs) will be useful if the practical situation focuses more on the set size. Most ofthe known constructions of MOCSs and ZCCSs based on generalized Boolean functions (GBFs) have lengths with the form of 2m or 2m+2t. Some constructions of MOCSs and ZCCSs based on other methods mostly have restrictive lengths. In this paper, we not only present constructions of an optimal ZCCS, but also construct MOCSs with flexible lengths. Both these constructions are based on extended Boolean functions. Though our proposed constructions generalize several previously known methods, we show that the parameters of these constructions are new and include previous parameters as special cases. In addition, a wide range of q-ary MOCSs and ZCCSs can be obtained by assigning different values to q.

show abstract

Section: Case 1: Ifmentioning

confidence: 99%

Section: Comparisonmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

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

Xiao

Cao

2022

Preprint

View full text Add to dashboard Cite

show abstract

“…is more adaptable than the set size of 2D-ZCACS given in [10]. Unlike [10], the proposed 2D-ZCACS can be reduced to 1D-ZCCS [11][12][13][14][15][16][17][18] also. As a result, many existing optimal 1D-ZCCSs have become special cases of the proposed construction [16][17][18].…”

Section: Introductionmentioning

confidence: 99%

A Direct Construction of Optimal 2D-ZCACS with Flexible Array Size and Large Set Size

Ghosh

Majhi

Paul

2023

Preprint

View full text Add to dashboard Cite

In this paper, we propose a direct construction of optimal two-dimensional Z-complementary array code sets (2D-ZCACS) using multivariable functions (MVFs). In contrast to earlier works, the proposed construction allows for a flexible array size and a large set size. Additionally, the proposed design can be transformed into a one-dimensional Z-complementary code set (1D-ZCCS). Many of the 1D-ZCCS described in the literature appeared to be special cases of this proposed construction. At last, we compare our work with the current state of the art and then draw our conclusions.

show abstract

New results on large sets of orthogonal arrays and orthogonal arrays

Chen,

Niu,

Shi

2024

J of Combinatorial Designs

View full text Add to dashboard Cite

Orthogonal array and a large set of orthogonal arrays are important research objects in combinatorial design theory, and they are widely applied to statistics, computer science, coding theory, and cryptography. In this paper, some new series of large sets of orthogonal arrays are given by direct construction, juxtaposition construction, Hadamard construction, finite field construction, and difference matrix construction. Subsequently, many new infinite classes of orthogonal arrays are obtained by using these large sets of orthogonal arrays and Kronecker product.

show abstract

New constructions of Z-complementary code sets and mutually orthogonal complementary sequence sets

Cited by 15 publications

References 36 publications

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

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

A Direct Construction of Optimal 2D-ZCACS with Flexible Array Size and Large Set Size

New results on large sets of orthogonal arrays and orthogonal arrays

Contact Info

Product

Resources

About