We complete the description of the procedure of topological expansion of a bipartite graph without parallel branches on the plane of changing the structure of cycles of length up to 10 inclusive. Based on previous papers, we have extended a set of theorems specifying transformation rules for cycles and paths when passing from a protograph to the Tanner graph. We propose a procedure for detecting the existence of a cycle of length 10 in the expanded graph by analyzing the protograph.

中文翻译：

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基于原型分析的QC-LDPC码Tanner图中长度10的循环检测

我们完成了对二部图的拓扑扩展过程的描述，该图在长度不超过10的循环结构改变平面上不具有平行分支。在以前的论文的基础上，我们扩展了一组定理，指定了从原型到Tanner图时循环和路径的变换规则。我们提出了一种通过分析原型来检测扩展图中长度为10的循环的存在的过程。