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Z-complementary pairs (ZCPs) were proposed by Fan et al. to make up for the scarcity of Golay complementary pairs. A ZCP of odd length *N* is called Z-*optimal* if its zero correlation zone width can achieve the maximum value (*N* + 1)/2. In this letter, inserting three elements to a GCP of length *L*, or deleting a point of a GCP of length *L*, we propose two constructions of Z-*optimal* ZCPs with length *L* + 3 and *L* - 1, where *L*=2^{α} 10^{β} 26^{γ}, α ≥ 1, β ≥ 0, γ ≥ 0 are integers. The proposed constructions generate ZCPs with new lengths which cannot be produced by earlier ones.

- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E104-A No.4 pp.768-772

- Publication Date
- 2021/04/01

- Publicized
- 2020/09/28

- Online ISSN
- 1745-1337

- DOI
- 10.1587/transfun.2020EAL2069

- Type of Manuscript
- LETTER

- Category
- Communication Theory and Signals

Shucong TIAN

Southwest Jiaotong University

Meng YANG

Southwest Jiaotong University

Jianpeng WANG

Southwest Jiaotong University

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Shucong TIAN, Meng YANG, Jianpeng WANG, "Two Constructions of Binary Z-Complementary Pairs" in IEICE TRANSACTIONS on Fundamentals,
vol. E104-A, no. 4, pp. 768-772, April 2021, doi: 10.1587/transfun.2020EAL2069.

Abstract: Z-complementary pairs (ZCPs) were proposed by Fan et al. to make up for the scarcity of Golay complementary pairs. A ZCP of odd length *N* is called Z-*optimal* if its zero correlation zone width can achieve the maximum value (*N* + 1)/2. In this letter, inserting three elements to a GCP of length *L*, or deleting a point of a GCP of length *L*, we propose two constructions of Z-*optimal* ZCPs with length *L* + 3 and *L* - 1, where *L*=2^{α} 10^{β} 26^{γ}, α ≥ 1, β ≥ 0, γ ≥ 0 are integers. The proposed constructions generate ZCPs with new lengths which cannot be produced by earlier ones.

URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.2020EAL2069/_p

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@ARTICLE{e104-a_4_768,

author={Shucong TIAN, Meng YANG, Jianpeng WANG, },

journal={IEICE TRANSACTIONS on Fundamentals},

title={Two Constructions of Binary Z-Complementary Pairs},

year={2021},

volume={E104-A},

number={4},

pages={768-772},

abstract={Z-complementary pairs (ZCPs) were proposed by Fan et al. to make up for the scarcity of Golay complementary pairs. A ZCP of odd length *N* is called Z-*optimal* if its zero correlation zone width can achieve the maximum value (*N* + 1)/2. In this letter, inserting three elements to a GCP of length *L*, or deleting a point of a GCP of length *L*, we propose two constructions of Z-*optimal* ZCPs with length *L* + 3 and *L* - 1, where *L*=2^{α} 10^{β} 26^{γ}, α ≥ 1, β ≥ 0, γ ≥ 0 are integers. The proposed constructions generate ZCPs with new lengths which cannot be produced by earlier ones.},

keywords={},

doi={10.1587/transfun.2020EAL2069},

ISSN={1745-1337},

month={April},}

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TY - JOUR

TI - Two Constructions of Binary Z-Complementary Pairs

T2 - IEICE TRANSACTIONS on Fundamentals

SP - 768

EP - 772

AU - Shucong TIAN

AU - Meng YANG

AU - Jianpeng WANG

PY - 2021

DO - 10.1587/transfun.2020EAL2069

JO - IEICE TRANSACTIONS on Fundamentals

SN - 1745-1337

VL - E104-A

IS - 4

JA - IEICE TRANSACTIONS on Fundamentals

Y1 - April 2021

AB - Z-complementary pairs (ZCPs) were proposed by Fan et al. to make up for the scarcity of Golay complementary pairs. A ZCP of odd length *N* is called Z-*optimal* if its zero correlation zone width can achieve the maximum value (*N* + 1)/2. In this letter, inserting three elements to a GCP of length *L*, or deleting a point of a GCP of length *L*, we propose two constructions of Z-*optimal* ZCPs with length *L* + 3 and *L* - 1, where *L*=2^{α} 10^{β} 26^{γ}, α ≥ 1, β ≥ 0, γ ≥ 0 are integers. The proposed constructions generate ZCPs with new lengths which cannot be produced by earlier ones.

ER -