A construction of strongly regular Cayley graphs and their applications to codebooks
In this paper, we give a kind of strongly regular Cayley graphs and a class of codebooks. Both constructions are based on choosing subsets of finite fields, and the main tools that we employed are Gauss sums. In particular, these obtained codebooks are asymptotically optimal with respect to the Welc...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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AIMS Press
2024-01-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.2024132?viewType=HTML |
| _version_ | 1827380497796300800 |
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| author | Yang Yan Xingguo Zhang Rize Jin Limin Zhou |
| author_facet | Yang Yan Xingguo Zhang Rize Jin Limin Zhou |
| author_sort | Yang Yan |
| collection | DOAJ |
| description | In this paper, we give a kind of strongly regular Cayley graphs and a class of codebooks. Both constructions are based on choosing subsets of finite fields, and the main tools that we employed are Gauss sums. In particular, these obtained codebooks are asymptotically optimal with respect to the Welch bound and they have new parameters. |
| first_indexed | 2024-03-08T13:33:47Z |
| format | Article |
| id | doaj.art-d33afc24031b4df4bb90bab1db46dcc6 |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-03-08T13:33:47Z |
| publishDate | 2024-01-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-d33afc24031b4df4bb90bab1db46dcc62024-01-17T01:23:35ZengAIMS PressAIMS Mathematics2473-69882024-01-01922672268310.3934/math.2024132A construction of strongly regular Cayley graphs and their applications to codebooksYang Yan0 Xingguo Zhang 1Rize Jin2Limin Zhou31. School of Information Technology and Engineering, Tianjin University of Technology and Education, Tianjin 300222, China2. Engineering Research Center of Integration and Application of Digital Learning Technology, Ministry of Education, Beijing 100039, China 3. School of Humanities, Tiangong University, Tianjin 300387, China4. School of Software, Tiangong University, Tianjin 300387, China 5. Tianjin Key Laboratory of Autonomous Intelligence Technology and Systems, Tianjin 300387, China6. Department of Mathematics, Binzhou University, Binzhou 256600, Shandong Province, ChinaIn this paper, we give a kind of strongly regular Cayley graphs and a class of codebooks. Both constructions are based on choosing subsets of finite fields, and the main tools that we employed are Gauss sums. In particular, these obtained codebooks are asymptotically optimal with respect to the Welch bound and they have new parameters.https://www.aimspress.com/article/doi/10.3934/math.2024132?viewType=HTMLcodebooksstrongly regular cayley graphsfinite fieldsgauss sumswelch bound |
| spellingShingle | Yang Yan Xingguo Zhang Rize Jin Limin Zhou A construction of strongly regular Cayley graphs and their applications to codebooks AIMS Mathematics codebooks strongly regular cayley graphs finite fields gauss sums welch bound |
| title | A construction of strongly regular Cayley graphs and their applications to codebooks |
| title_full | A construction of strongly regular Cayley graphs and their applications to codebooks |
| title_fullStr | A construction of strongly regular Cayley graphs and their applications to codebooks |
| title_full_unstemmed | A construction of strongly regular Cayley graphs and their applications to codebooks |
| title_short | A construction of strongly regular Cayley graphs and their applications to codebooks |
| title_sort | construction of strongly regular cayley graphs and their applications to codebooks |
| topic | codebooks strongly regular cayley graphs finite fields gauss sums welch bound |
| url | https://www.aimspress.com/article/doi/10.3934/math.2024132?viewType=HTML |
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