基于种子位交换禁忌搜索的常重码新下界
New lower bounds for constant-weight codes via seeded bit-swap tabu search
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中文总结 AI 辅助
该研究采用种子位交换禁忌搜索构造出124种二元常重码，改进了其最大规模的下界，同时提升了对应n值下kissing数的下界。
中文摘要 AI 辅助
二元常重码是长度为n的二元字集合，其中每个字的汉明重量均为w，且集合中任意两个字的汉明距离至少为d。A(n,d,w)表示参数为(n,d,w)的二元常重码的最大规模。通过种子初始化结合位交换禁忌搜索，我们得到124种新构造，改进了A(n,d,w)的现有下界。作为n∈{32,33,34,37}时A(n,8,8)更强下界的推论，我们还改进了kissing数τ₃₂、τ₃₃、τ₃₄和τ₃₇的下界。
英文摘要
A binary constant-weight code is a set of binary words of length $n$ such that each word has exactly weight $w$ and is at least Hamming distance $d$ from every other word in the set. $A(n,d,w)$ denotes the maximum size of a binary constant-weight code with parameters $(n,d,w)$. Using seeded initialization with bit-swap tabu search, we found 124 new constructions that improve existing lower bounds for $A(n,d,w)$. As a corollary of stronger bounds on $A(n,8,8)$ for $n \in \{ 32,33,34,37 \}$, we also improve lower bounds on kissing numbers $τ_{32}$, $τ_{33}$, $τ_{34}$, and $τ_{37}$.
