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arXiv · 2603.00174

Automated Discovery of Improved Constant Weight Binary Codes

Christopher D. Rosin
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Abstract

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.

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Christopher D. Rosin. 2026-02-26. Automated Discovery of Improved Constant Weight Binary Codes. https://arxiv.org/abs/2603.00174

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