Semidefinite programming bounds for few-distance sets in the Hamming and Johnson spaces

We study the maximum cardinality problem of a set of few distances in the Hamming and Johnson spaces. We formulate semidefinite programs for this problem and extend the 2011 works by Barg-Musin and Musin-Nozaki. As our main result, we find new parameters for which the maximum size of two- and three-...

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Bibliographic Details
Published in:arXiv.org 2022-07
Main Authors: Barg, Alexander, Ching-Yi, Lai, Tseng, Pin-Chieh, Wei-Hsuan, Yu
Format: Article
Language:English
Subjects:
Semidefinite programming
Online Access:Get full text
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Summary:We study the maximum cardinality problem of a set of few distances in the Hamming and Johnson spaces. We formulate semidefinite programs for this problem and extend the 2011 works by Barg-Musin and Musin-Nozaki. As our main result, we find new parameters for which the maximum size of two- and three-distance sets is known exactly.
ISSN:2331-8422