论文标题
分裂Terwilliger代数的二进制代码的半决赛编程范围
Semidefinite programming bounds for binary codes from a split Terwilliger algebra
论文作者
论文摘要
我们研究$ a（n，d）$的上限，这是长度$ n $和锤击距离至少$ d $的代码字的最大尺寸。 Schrijver研究了锤子计划的Terwilliger代数，并提出了一个半决赛计划，以约束$ a（n，d）$。我们基于分裂的Terwilliger代数来得出更复杂的矩阵不平等，以提高Schrijver的半趋势编程界限，以$ a（n，d）$。特别是，我们将$ a（18,4）$的半决赛编程范围提高到$ 6551 $。
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 $6551$.
