2026-09-20T14:13:01Zhttps://dspace.mit.edu/server/oai/requestoai:dspace.mit.edu:1721.1/1474852023-01-20T03:01:02Zcom_1721.1_7582com_1721.1_7581col_1721.1_131022
Cohn, Henry
Zhang, Yichi
Massachusetts Institute of Technology. Department of Mathematics
2023-01-19T19:53:33Z
2023-01-19T19:53:33Z
2022-09
2022-09-12T15:08:54.299Z
https://hdl.handle.net/1721.1/147485
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.
Massachusetts Institute of Technology
In Copyright - Educational Use Permitted
Copyright MIT
http://rightsstatements.org/page/InC-EDU/1.0/
A Solution of the Energy Minimization Problem for Codes of Codimension 1
Thesis
application/pdf
Doctoral
Doctor of Philosophy
Publication
unknown
unknown
<Publication xmlns="https://www.openaire.eu/cerif-profile/1.1/" id="fdd33c72-956f-4161-a453-0f47082b0cbe">
<Type xmlns="https://www.openaire.eu/cerif-profile/vocab/COAR_Publication_Types">http://purl.org/coar/resource_type/c_1843</Type>
<Title>A Solution of the Energy Minimization Problem for Codes of Codimension 1</Title>
<PublishedIn>
<Publication>
</Publication>
</PublishedIn>
<PublicationDate>2022-09</PublicationDate>
<Authors>
<Author>
<DisplayName>Zhang, Yichi</DisplayName>
<Affiliation>
<OrgUnit>
</OrgUnit>
</Affiliation>
</Author>
</Authors>
<Editors>
</Editors>
<Publishers>
<Publisher>
<DisplayName>Massachusetts Institute of Technology</DisplayName>
<OrgUnit />
</Publisher>
</Publishers>
<License>http://rightsstatements.org/page/InC-EDU/1.0/</License>
<Abstract>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.</Abstract>
<Access xmlns="http://purl.org/coar/access_right"
>
</Access>
</Publication>