用自动搜索法找到24组更优的二进制码，提升纠错能力上限。
Automated Discovery of Improved Constant Weight Binary Codes
- 基于位交换与随机评分距离直方图的贪心搜索策略
- 对24组参数在6≤d≤18、18≤n≤35下提升码长下界
- 适合编码理论与组合设计研究者参考
常重二进制码由n比特二进制码字组成，每个码字恰好有w个1位，且任意两码字间汉明距离不小于d。A(n,d,w)表示该类码的最大数量。本文通过构造新码，对24组参数（n,d,w）在6≤d≤18、18≤n≤35范围内建立了更优的A(n,d,w)下界。改进方法包括：一种在位交换层面运行的禁忌搜索；以及一种新颖的贪心启发式，每次选择使与已添加码字距离直方图得分最高的候选码字。上述策略由自动化协议CPro1生成、实现并测试。
原文摘要 · Abstract (English)
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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