{"id":{"repo_id":"mit","oai_identifier":"oai:dspace.mit.edu:1721.1/156990"},"canonical_url":"https://search.dev.ndltd.org/etd/mit/oai:dspace.mit.edu:1721.1/156990","repository":{"repo_id":"mit","name":"MIT","base_url":"https://dspace.mit.edu/oai/request"},"display":{"title":"Semidefinite programming bounds for codes in complex projective space","abstract":"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.","abstract_html":"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.","abstract_has_math":false,"creators":["Li, Rupert"],"institution":"Massachusetts Institute of Technology","degree_name":"Master","degree_level":null,"degree_discipline":null,"degree_department":"Massachusetts Institute of Technology. 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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."]},{"key":"dc:description.degree","label":"Dc Description Degree","values":["MNG"]},{"key":"dc:title","label":"Title","values":["Semidefinite programming bounds for codes in complex projective space"]}]}],"canonical_facts":{"dc:contributor.advisor":["Cohn, Henry","Sun, Nike"],"dc:contributor.department":["Massachusetts Institute of Technology. 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We present some numerical computations that demonstrate, in some test examples, that our three-point bounds improve upon two-point bounds."],"dc:description.degree":["MNG"],"dc:identifier.uri":["https://hdl.handle.net/1721.1/156990"],"dc:publisher":["Massachusetts Institute of Technology"],"dc:rights":["In Copyright - Educational Use Permitted","Copyright retained by author(s)"],"dc:rights.uri":["https://rightsstatements.org/page/InC-EDU/1.0/"],"dc:title":["Semidefinite programming bounds for codes in complex projective space"],"dc:type":["Thesis"],"thesis:degree_name":["Master"]},"updated_at":"2026-07-22T22:22:06Z"}