New lower bounds for constant-weight codes via seeded bit-swap tabu search

Abstract

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 $τ_{37}$.