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 |
| Summary: | 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. |
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