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A Solution of the Energy Minimization Problem for Codes of Codimension 1

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Zhang-yichi-phd-math-2022-thesis.pdf

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Author(s)
Zhang, Yichi
Advisor(s)
Cohn, Henry
Date Issued
September 2022
Publisher
Massachusetts Institute of Technology
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.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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