Automated Discovery of Improved Constant Weight Binary Codes
This work provides incremental improvements to the known bounds for a specific type of error-correcting code, which could be useful for researchers and practitioners working with constant weight codes.
This paper improves lower bounds on $A(n,d,w)$ for constant weight binary codes by constructing new, larger codes. They achieved this for 24 specific $(n,d,w)$ values where $6 \leq d \leq 18$ and $18 \leq n \leq 35$.
A constant weight binary code consists of $n$-bit binary codewords, each with exactly $w$ bits equal to 1, such that any two codewords are at least Hamming distance $d$ apart. $A(n,d,w)$ is the maximum size of a constant weight binary code with parameters $n,d,w$. We establish improved lower bounds on $A(n,d,w)$ by constructing new larger codes, for 24 values of $(n,d,w)$ with $6 \leq d \leq 18$ and $18 \leq n \leq 35$. The improved lower bounds come from two strategies. The first is a tabu search that operates at the level of bit swaps. The second is a novel greedy heuristic that repeatedly chooses the candidate codeword that maximizes a randomly-scored histogram of distances to previously-added codewords. These strategies were proposed by CPro1, an automated protocol that generates, implements, and tests diverse strategies for combinatorial constructions.