Semidefinite programming bounds for binary codes from a split Terwilliger algebra

We study the upper bounds for \(A(n,d)\), the maximum size of codewords with length \(n\) and Hamming distance at least \(d\). Schrijver studied the Terwilliger algebra of the Hamming scheme and proposed a semidefinite program to bound \(A(n, d)\). We derive more sophisticated matrix inequalities ba...

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Bibliographic Details
Published in:arXiv.org 2023-06
Main Authors: Tseng, Pin-Chieh, Ching-Yi, Lai, Wei-Hsuan, Yu
Format: Article
Language:English
Subjects:
Algebra
Binary codes
Codes
Mathematical analysis
Matrices (mathematics)
Semidefinite programming
Upper bounds
Online Access:Get full text
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Summary:We study the upper bounds for \(A(n,d)\), the maximum size of codewords with length \(n\) and Hamming distance at least \(d\). Schrijver studied the Terwilliger algebra of the Hamming scheme and proposed a semidefinite program to bound \(A(n, d)\). We derive more sophisticated matrix inequalities based on a split Terwilliger algebra to improve Schrijver's semidefinite programming bounds on \(A(n, d)\). In particular, we improve the semidefinite programming bounds on \(A(18,4)\) to \(6551\).
ISSN:2331-8422
DOI:10.48550/arxiv.2203.06568