发表机构
Universidade Federal do Rio de Janeiro; Universidade Estadual de Ponta Grossa（里约热内卢联邦大学; 蓬塔格罗萨州立大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出从书图构造线性码的新方法，通过2-和获得最优二元码，并利用拟阵与图论研究性质，进而将CSS码生成条件转化为拟阵理论，用循环图构造满足条件的码。
AI 中文摘要
在本文中，我们提出了一种由书图构造线性码的方法。应用该方法，我们通过两个相等书图的2-和构造出在其长度和维度下具有最大可能最小距离的二元码。随后，我们结合拟阵和图论来研究所得线性码的一些性质。此外，我们证明，从任意图的关联矩阵出发，我们可以在任何有限域上获得保持相同参数的线性码。进一步，我们展示了两个线性码生成Calderbank-Shor-Steane（CSS）码的条件如何转化为拟阵理论，并利用循环图，我们展示了一种生成满足该条件的码的方法。
英文摘要
In this paper, we present a method for constructing linear codes derived from book graphs. Applying such a method, we construct binary codes that have the greatest possible minimum distance for their length and dimension by means of the $2$-sum of two equal book graphs. We then utilize matroid and graph theory together to investigate some properties of the resulting linear codes. Furthermore, we show that, from the incidence matrix of any graph, we can obtain a linear code over any finite field maintaining the same parameters. Furthermore, we show how the condition for two linear codes to generate a Calderbank-Shor-Steane (CSS) code translates into matroid theory and, utilizing cycle graphs, we exhibit a way to generate codes that meet this condition.
Comments19 pages, 4 figures
