Construction of new even-length type-II Z-complementary pair

Construction of new even-length type-II Z-complementary pair

To enrich the parameter forms of Z-complementary pair (ZCP), the constructions of new Type-II ZCP were investigated.First, Type-II <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML"> <mrow><mo>(</mo> <mrow> <msup> <mn>2<...

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Bibliographic Details
Main Authors: Xiaoyu CHEN, Lianfeng SUN, Jiekun ZHANG, Yubo LI
Format: Article
Language:zho
Published: Editorial Department of Journal on Communications 2023-03-01
Series:Tongxin xuebao
Subjects:
aperiodic
iterative method
Golay complementary pair
Z-complementary pair
Online Access:http://www.joconline.com.cn/zh/article/doi/10.11959/j.issn.1000-436x.2023052/
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Summary:To enrich the parameter forms of Z-complementary pair (ZCP), the constructions of new Type-II ZCP were investigated.First, Type-II <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML"> <mrow><mo>(</mo> <mrow> <msup> <mn>2</mn> <mrow> <mi>k</mi><mo>+</mo><mn>2</mn></mrow> </msup> <mi>N</mi><mo>,</mo><mo stretchy="false">(</mo><msup> <mn>2</mn> <mrow> <mi>k</mi><mo>+</mo><mn>2</mn></mrow> </msup> <mo>−</mo><mn>1</mn><mo stretchy="false">)</mo><mi>N</mi></mrow> <mo>)</mo></mrow><mo>−</mo><mtext>ZCP</mtext></math></inline-formula> was proposed by using iterative method.When N= 1, Z-optimal type-II <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML"> <mrow><mo>(</mo> <mrow> <msup> <mn>2</mn> <mrow> <mi>k</mi><mo>+</mo><mn>2</mn></mrow> </msup> <mo>,</mo><mo stretchy="false">(</mo><msup> <mn>2</mn> <mrow> <mi>k</mi><mo>+</mo><mn>2</mn></mrow> </msup> <mo>−</mo><mn>1</mn><mo stretchy="false">)</mo></mrow> <mo>)</mo></mrow><mo>−</mo><mtext>ZCP</mtext></math></inline-formula> could be obtained.Then, type-II <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML"> <mrow><mo>(</mo> <mrow> <msup> <mn>2</mn> <mrow> <mi>k</mi><mo>+</mo><mn>1</mn></mrow> </msup> <mi>N</mi><mo>+</mo><msup> <mn>2</mn> <mrow> <mi>k</mi><mo>+</mo><mn>1</mn></mrow> </msup> <mo>,</mo><msup> <mn>2</mn> <mrow> <mi>k</mi><mo>+</mo><mn>1</mn></mrow> </msup> <mi>N</mi><mo>+</mo><msup> <mn>2</mn> <mrow> <mi>k</mi><mo>+</mo><mn>1</mn></mrow> </msup> <mo>−</mo><mfrac> <mi>N</mi> <mn>2</mn> </mfrac> </mrow> <mo>)</mo></mrow><mo>−</mo><mtext>ZCP</mtext></math></inline-formula> was presented by combining the iterative method with the insertion method.When N= 2, Z-optimal type-II <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML"> <mrow><mo>(</mo> <mrow> <mn>3</mn><mo>×</mo><msup> <mn>2</mn> <mrow> <mi>k</mi><mo>+</mo><mn>1</mn></mrow> </msup> <mo>,</mo><mn>3</mn><mo>×</mo><msup> <mn>2</mn> <mrow> <mi>k</mi><mo>+</mo><mn>1</mn></mrow> </msup> <mo>−</mo><mn>1</mn></mrow> <mo>)</mo></mrow><mo>−</mo><mtext>ZCP</mtext></math></inline-formula> could be obtained.The proposed constructions can generate new even-length ZCP, and expand the number of existing ZCP.
ISSN:1000-436X

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