论文标题
公平[[2,10]，[6,6]] - 12立方的分区
Equitable [[2,10],[6,6]]-partitions of the 12-cube
论文作者
论文摘要
我们描述了与商矩阵$ [[2,10]，[6,6] $的计算机辅助分区的计算机辅助分类，或同等地，简单的简单正交阵列OA $（1536,12,2,2,7）$（1536,12,2,7）$，或订单 - $ 7 $ 7 $ corsor-ymmmune-ymmune-ymmune boolevient $ 12 $ 153 $ 153 $ 153 $ 153 $ variables（不平衡订单-7 $相关 - 免疫布尔功能$ 12 $变量）。我们发现，所考虑的对象有$ 103 $的同等类别，其中只有两个几乎是OA $（1536,12,2,8）$。此外，我们发现有40美元的等价类别的差异简单的简单oa $（1536,12,2,7）$（等效地，公平的分区，$ 12 $ -CUBE，带有商矩阵$ [[2,6,4]，[6,2,4]，[6,2,4]，[6,6,6,0] $），[6,6,6,0] $） oa $（1536,12,2,7）$。 关键字：正交阵列，相关 - 免疫布尔功能，公平分区，完美的色彩，有趣的集合。
We describe the computer-aided classification of equitable partitions of the $12$-cube with quotient matrix $[[2,10],[6,6]]$, or, equivalently, simple orthogonal arrays OA$(1536,12,2,7)$, or order-$7$ correlation-immune Boolean functions in $12$ variables with $1536$ ones (which completes the classification of unbalanced order-$7$ correlation-immune Boolean functions in $12$ variables). We find that there are $103$ equivalence classes of the considered objects, and there are only two almost-OA$(1536,12,2,8)$ among them. Additionally, we find that there are $40$ equivalence classes of pairs of disjoint simple OA$(1536,12,2,7)$ (equivalently, equitable partitions of the $12$-cube with quotient matrix $[[2,6,4], [6,2,4], [6,6,0]]$) and discuss the existence of a non-simple OA$(1536,12,2,7)$. Keywords: orthogonal arrays, correlation-immune Boolean functions, equitable partitions, perfect colorings, intriguing sets.
