二元等重码的新下界：\(A(23,6,10)\geq 2979\) 且 \(A(24,6,10)\geq 4214\)
New lower bounds for binary constant-weight codes: $A(23,6,10)\geq 2979$ and $A(24,6,10)\geq 4214$
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中文总结 AI 辅助
本文通过构建显式码证明\(A(23,6,10)\geq 2979\)和\(A(24,6,10)\geq 4214\)，改进了之前最好的显式码规模。构造方法采用坐标分解，利用CHILS从全交叉兼容池中选择互补部分，还得到了其他相关码的规模，发布了代码文件等。
中文摘要 AI 辅助
设\(A(n,d,w)\)表示长度为\(n\)、最小距离为\(d\)且权重为\(w\)的二元等重码的最大规模。本文通过构建显式码证明了\(A(23,6,10)\geq 2979\)和\(A(24,6,10)\geq 4214\)，改进了之前最好的显式码规模，并超过了相应的界。还得到了\(A(23,6,11)\geq 3539\)和\(A(24,6,8)\geq 1855\)。构造方法采用坐标分解，利用CHILS从全交叉兼容池中选择互补部分。对\(A(23,6,10)\)的现有码进行精确计算，证明了插入最大化并排除了至多删除三个码字的改进交换。分析了素数阶置换下不变的码，排除了几种循环类型，给出了部分类型的启发式饱和证据。最后发布了代码文件、独立验证器、模型描述和计算日志。
英文摘要
Let $A(n,d,w)$ denote the maximum size of a binary constant-weight code of length $n$, minimum distance $d$, and weight $w$. We construct explicit codes proving $A(23,6,10)\ge 2979$ and $A(24,6,10)\ge 4214$. These improve the best surviving explicit codes of sizes 2969 and 4174 and surpass the corresponding 1990 bounds 2970 and 4200 of Brouwer, Shearer, Sloane and Smith, whose code listings were lost. We also obtain $A(23,6,11)\ge 3539$ and $A(24,6,8)\ge 1855$. All four bounds are now listed in Brouwer's online table. The constructions use a coordinate decomposition in which one half is fixed to a known code and the complementary half is selected from its full cross-compatible pool using CHILS for maximum-weight independent set. For the 2969-word $A(23,6,10)$ incumbent, exact computations with two solver families prove insertion maximality and exclude every improving exchange deleting at most three codewords. We also analyze codes invariant under prime-order permutations: several cycle types are excluded exactly, the $5+1^{18}$ type has upper bound 499, and reproducible heuristic saturation evidence is reported for the remaining types, with $13+1^{10}$ left open. Code files, an independent validator, model descriptions, and computational logs are released.
