How to Construct Mutually Orthogonal Complementary Sets with Non-Power-of-Two Lengths?

Shing Wei Wu; Chao Yu Chen; Zilongs Liu

doi:10.1109/TIT.2020.2980818

How to Construct Mutually Orthogonal Complementary Sets with Non-Power-of-Two Lengths?

Shing Wei Wu, Chao Yu Chen, Zilongs Liu

Department of Electrical Engineering

Research output: Contribution to journal › Article › peer-review

19 Citations (Scopus)

Abstract

Mutually orthogonal complementary sets (MOCSs) have received significant research attention in recent years due to their wide applications in communications and radar. Existing MOCSs which are constructed based on generalized Boolean functions (GBFs) mostly have lengths of power-of-two. How to construct MOCSs with non-power-of-two lengths whilst having large set sizes is a largely open problem. With the aid of GBFs, in this paper, we present new constructions of such MOCSs and show that the maximal achievable set size is 1/2 of the flock size of an MOCS.

Original language	English
Article number	9036980
Pages (from-to)	3464-3472
Number of pages	9
Journal	IEEE Transactions on Information Theory
Volume	67
Issue number	6
DOIs	https://doi.org/10.1109/TIT.2020.2980818
Publication status	Published - 2021 Jun

All Science Journal Classification (ASJC) codes

Information Systems
Computer Science Applications
Library and Information Sciences

Access to Document

10.1109/TIT.2020.2980818

Cite this

@article{9dc1e7a9d11a47e5a10e7857a1af6461,

title = "How to Construct Mutually Orthogonal Complementary Sets with Non-Power-of-Two Lengths?",

abstract = "Mutually orthogonal complementary sets (MOCSs) have received significant research attention in recent years due to their wide applications in communications and radar. Existing MOCSs which are constructed based on generalized Boolean functions (GBFs) mostly have lengths of power-of-two. How to construct MOCSs with non-power-of-two lengths whilst having large set sizes is a largely open problem. With the aid of GBFs, in this paper, we present new constructions of such MOCSs and show that the maximal achievable set size is 1/2 of the flock size of an MOCS.",

author = "Wu, {Shing Wei} and Chen, {Chao Yu} and Zilongs Liu",

note = "Funding Information: Manuscript received October 15, 2019; accepted February 14, 2020. Date of publication March 16, 2020; date of current version May 20, 2021. The work of Shing-Wei Wu and Chao-Yu Chen was supported in part by the Ministry of Science and Technology, Taiwan, China, under Grant MOST 107-2221-E-006-065-MY2. (Corresponding author: Chao-Yu Chen.) Shing-Wei Wu and Chao-Yu Chen are with the Department of Engineering Science, National Cheng Kung University, Tainan 70101, Taiwan (e-mail: [email protected]; [email protected]). Publisher Copyright: {\textcopyright} 1963-2012 IEEE.",

year = "2021",

month = jun,

doi = "10.1109/TIT.2020.2980818",

language = "English",

volume = "67",

pages = "3464--3472",

journal = "IEEE Transactions on Information Theory",

issn = "0018-9448",