Semidefinite programming bounds for binary codes from a split Terwilliger algebra

Pin Chieh Tseng*, Ching Yi Lai, Wei Hsuan Yu

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

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.

Original languageEnglish
JournalDesigns, Codes, and Cryptography
DOIs
StateAccepted/In press - 2023

Keywords

  • Binary codes
  • Distance distribution
  • Semidefinite program
  • Terwilliger algebra
  • Weight enumeration

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