Semidefinite programming bounds for codes in complex projective space
We establish three-point bounds for codes in complex projective space, where previously only two-point linear programming bounds were known. We discuss how these bounds can be computed numerically using semidefinite programming, and provide a framework that allows for proofs of universal optimality...
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| Format: | Thesis |
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Massachusetts Institute of Technology
2024
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| Online Access: | https://hdl.handle.net/1721.1/156990 |
| _version_ | 1824458326240395264 |
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| author | Li, Rupert |
| author2 | Cohn, Henry |
| author_facet | Cohn, Henry Li, Rupert |
| author_sort | Li, Rupert |
| collection | MIT |
| description | We establish three-point bounds for codes in complex projective space, where previously only two-point linear programming bounds were known. We discuss how these bounds can be computed numerically using semidefinite programming, and provide a framework that allows for proofs of universal optimality through solving finitely many semidefinite programs. We present some numerical computations that demonstrate, in some test examples, that our three-point bounds improve upon two-point bounds. |
| first_indexed | 2025-02-19T04:24:07Z |
| format | Thesis |
| id | mit-1721.1/156990 |
| institution | Massachusetts Institute of Technology |
| last_indexed | 2025-02-19T04:24:07Z |
| publishDate | 2024 |
| publisher | Massachusetts Institute of Technology |
| record_format | dspace |
| spelling | mit-1721.1/1569902024-09-25T03:16:31Z Semidefinite programming bounds for codes in complex projective space Li, Rupert Cohn, Henry Sun, Nike Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science We establish three-point bounds for codes in complex projective space, where previously only two-point linear programming bounds were known. We discuss how these bounds can be computed numerically using semidefinite programming, and provide a framework that allows for proofs of universal optimality through solving finitely many semidefinite programs. We present some numerical computations that demonstrate, in some test examples, that our three-point bounds improve upon two-point bounds. MNG 2024-09-24T18:25:21Z 2024-09-24T18:25:21Z 2024-05 2024-07-11T14:37:40.168Z Thesis https://hdl.handle.net/1721.1/156990 In Copyright - Educational Use Permitted Copyright retained by author(s) https://rightsstatements.org/page/InC-EDU/1.0/ application/pdf Massachusetts Institute of Technology |
| spellingShingle | Li, Rupert Semidefinite programming bounds for codes in complex projective space |
| title | Semidefinite programming bounds for codes in complex projective space |
| title_full | Semidefinite programming bounds for codes in complex projective space |
| title_fullStr | Semidefinite programming bounds for codes in complex projective space |
| title_full_unstemmed | Semidefinite programming bounds for codes in complex projective space |
| title_short | Semidefinite programming bounds for codes in complex projective space |
| title_sort | semidefinite programming bounds for codes in complex projective space |
| url | https://hdl.handle.net/1721.1/156990 |
| work_keys_str_mv | AT lirupert semidefiniteprogrammingboundsforcodesincomplexprojectivespace |