Solov'eva-Phelps码的SQS-图
SQS-graphs of Solov'eva-Phelps codes
摘要：
二进制扩展1-完美码$\mathcal C$通过与其码字相关联的Steiner四元组系统折叠在其内核上。由此产生的折叠，提出作为一个图形不变的$\mathcal C$，区分之间的361个非线性代码$\mathcal C$的内核尺寸$κ$通过Solov'eva-Phelps加倍建设，其中$9\geqκ\geq 5$。361个结果图中的每一个都有其大部分非循环边可表示为长度为8的扩展1-完美分区（由菲尔普斯分类）的类的乘积的字典序四分之一，而循环大多可表示为法诺平面的线。
英文摘要：
A binary extended 1-perfect code $\mathcal C$ folds over its kernel via the Steiner quadruple systems associated with its codewords. The resulting folding, proposed as a graph invariant for $\mathcal C$, distinguishes among the 361 nonlinear codes $\mathcal C$ of kernel dimension $κ$ obtained via Solov'eva-Phelps doubling construction, where $9\geqκ\geq 5$. Each of the 361 resulting graphs has most of its nonloop edges expressible in terms of lexicographically ordered quarters of products of classes from extended 1-perfect partitions of length 8 (as classified by Phelps) and loops mostly expressible in terms of the lines of the Fano plane.
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