AI 中文总结
研究编码理论与图论中运算联系，以二元线性码的哈斯图为基础，刻画扩展码、删截码及两码直和对应的图，建立码运算图与图特定运算的关系。
AI 中文摘要
本文探讨编码理论与图论中的运算以及这两个领域中的一些运算之间的联系。回顾了二元线性码\(\Gamma(C)\)的哈斯图概念，它直观地表示具有偏序的二元线性码的陪集。主要目标是以给定二元线性码的图为起点，刻画与扩展码、删截码以及两个码的直和相对应的图。建立了码运算的图与图的特定运算之间的关系。
英文摘要
This manuscript addresses a connection between operations in coding theory and graph theory, as well as some operations in both areas. The concept of the Hasse diagram of a binary linear code, $Γ(C)$, is recall; this concept visually represents the cosets of a binary linear code with a partial ordering. The main objetive is to give a characterization of the graphs corresponding to: extended codes, punctured codes, and the direct sum of two codes, using the graph of the given binary linear code as a starting point. Relationships are established between the graphs of code operations and particular operations of graphs.
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