Semidefinite programming bounds for binary codes from a split Terwilliger algebra
نویسندگان
چکیده
We study the upper bounds for $A(n,d)$, maximum size of codewords with length $n$ and Hamming distance at least $d$. Schrijver studied Terwilliger algebra scheme proposed a semidefinite program to bound $A(n, d)$. derive more sophisticated matrix inequalities based on split improve Schrijver's programming In particular, we $A(18,4)$ $6551$.
منابع مشابه
New upper bounds for nonbinary codes based on the Terwilliger algebra and semidefinite programming
We give a new upper bound on the maximum size Aq(n, d) of a code of word length n and minimum Hamming distance at least d over the alphabet of q ≥ 3 letters. By blockdiagonalizing the Terwilliger algebra of the nonbinary Hamming scheme, the bound can be calculated in time polynomial in n using semidefinite programming. For q = 3, 4, 5 this gives several improved upper bounds for concrete values...
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ژورنال
عنوان ژورنال: Designs, Codes and Cryptography
سال: 2023
ISSN: ['0925-1022', '1573-7586']
DOI: https://doi.org/10.1007/s10623-023-01250-4