A Solution of the Energy Minimization Problem for Codes of Codimension 1
In this thesis, we study the space of quasicodes using Delsarte’s linear programming bound to solve the energy minimization problem on codes. Our main contribution is we give the optimal code of codimension 1 for any potential function. We also investigate the polytope of quasicodes, where we give a...
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| Format: | Thesis |
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Massachusetts Institute of Technology
2023
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| Online Access: | https://hdl.handle.net/1721.1/147485 |
| _version_ | 1811098177589215232 |
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| author | Zhang, Yichi |
| author2 | Cohn, Henry |
| author_facet | Cohn, Henry Zhang, Yichi |
| author_sort | Zhang, Yichi |
| collection | MIT |
| description | In this thesis, we study the space of quasicodes using Delsarte’s linear programming bound to solve the energy minimization problem on codes. Our main contribution is we give the optimal code of codimension 1 for any potential function. We also investigate the polytope of quasicodes, where we give a symmetry and a list of vertices in some special cases. |
| first_indexed | 2024-09-23T17:11:07Z |
| format | Thesis |
| id | mit-1721.1/147485 |
| institution | Massachusetts Institute of Technology |
| last_indexed | 2024-09-23T17:11:07Z |
| publishDate | 2023 |
| publisher | Massachusetts Institute of Technology |
| record_format | dspace |
| spelling | mit-1721.1/1474852023-01-20T03:01:02Z A Solution of the Energy Minimization Problem for Codes of Codimension 1 Zhang, Yichi Cohn, Henry Massachusetts Institute of Technology. Department of Mathematics In this thesis, we study the space of quasicodes using Delsarte’s linear programming bound to solve the energy minimization problem on codes. Our main contribution is we give the optimal code of codimension 1 for any potential function. We also investigate the polytope of quasicodes, where we give a symmetry and a list of vertices in some special cases. Ph.D. 2023-01-19T19:53:33Z 2023-01-19T19:53:33Z 2022-09 2022-09-12T15:08:54.299Z Thesis https://hdl.handle.net/1721.1/147485 In Copyright - Educational Use Permitted Copyright MIT http://rightsstatements.org/page/InC-EDU/1.0/ application/pdf Massachusetts Institute of Technology |
| spellingShingle | Zhang, Yichi A Solution of the Energy Minimization Problem for Codes of Codimension 1 |
| title | A Solution of the Energy Minimization Problem for Codes of Codimension 1 |
| title_full | A Solution of the Energy Minimization Problem for Codes of Codimension 1 |
| title_fullStr | A Solution of the Energy Minimization Problem for Codes of Codimension 1 |
| title_full_unstemmed | A Solution of the Energy Minimization Problem for Codes of Codimension 1 |
| title_short | A Solution of the Energy Minimization Problem for Codes of Codimension 1 |
| title_sort | solution of the energy minimization problem for codes of codimension 1 |
| url | https://hdl.handle.net/1721.1/147485 |
| work_keys_str_mv | AT zhangyichi asolutionoftheenergyminimizationproblemforcodesofcodimension1 AT zhangyichi solutionoftheenergyminimizationproblemforcodesofcodimension1 |