Semidefinite programming bounds for binary codes from a split Terwilliger algebra

03/13/2022

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by   Pin-Chieh Tseng, et al.

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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) and A(19, 4) to 6551 and 13087, respectively.