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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| Language: | zho |
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Editorial Department of Journal on Communications
2023-03-01
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| Series: | Tongxin xuebao |
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| Online Access: | http://www.joconline.com.cn/zh/article/doi/10.11959/j.issn.1000-436x.2023052/ |
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| _version_ | 1841540055207772160 |
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| author | Xiaoyu CHEN Lianfeng SUN Jiekun ZHANG Yubo LI |
| author_facet | Xiaoyu CHEN Lianfeng SUN Jiekun ZHANG Yubo LI |
| author_sort | Xiaoyu CHEN |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-8ca9f1b858b14490a73ae11b0a6a7366 |
| institution | Kabale University |
| issn | 1000-436X |
| language | zho |
| publishDate | 2023-03-01 |
| publisher | Editorial Department of Journal on Communications |
| record_format | Article |
| series | Tongxin xuebao |
| spelling | doaj-art-8ca9f1b858b14490a73ae11b0a6a73662025-01-14T06:23:21ZzhoEditorial Department of Journal on CommunicationsTongxin xuebao1000-436X2023-03-014413814459387782Construction of new even-length type-II Z-complementary pairXiaoyu CHENLianfeng SUNJiekun ZHANGYubo LITo 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.http://www.joconline.com.cn/zh/article/doi/10.11959/j.issn.1000-436x.2023052/aperiodiciterative methodGolay complementary pairZ-complementary pair |
| spellingShingle | Xiaoyu CHEN Lianfeng SUN Jiekun ZHANG Yubo LI Construction of new even-length type-II Z-complementary pair Tongxin xuebao aperiodic iterative method Golay complementary pair Z-complementary pair |
| title | Construction of new even-length type-II Z-complementary pair |
| title_full | Construction of new even-length type-II Z-complementary pair |
| title_fullStr | Construction of new even-length type-II Z-complementary pair |
| title_full_unstemmed | Construction of new even-length type-II Z-complementary pair |
| title_short | Construction of new even-length type-II Z-complementary pair |
| title_sort | construction of new even length type ii z complementary pair |
| topic | aperiodic iterative method Golay complementary pair Z-complementary pair |
| url | http://www.joconline.com.cn/zh/article/doi/10.11959/j.issn.1000-436x.2023052/ |
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