We construct linear codes over the finite field Fq from arbitrary simplicial complexes, establishing a connection between topological properties and fundamental coding parameters. First, we study the behaviour of the weights of codewords from a geometric point of view, interpreting them in terms of the combinatorial structure of the associated simplicial complex. This approach allows us to describe the minimum distance of the codes in terms of certain geometric features of the complex. Subsequently, we analyse how various topological operations on simplicial complexes affect the classical parameters of the codes. This study leads to the formulation of geometric criteria that make it possible to explicitly control and manipulate these parameters. Finally, as an application of the obtained results, we construct several families of optimal linear codes over F2 using these geometric methods. Thanks to the previously established geometric properties, we can precisely determine the parameters of these families.

翻译：我们利用任意单纯复形在有限域Fq上构造线性码，建立了拓扑性质与基本编码参数之间的联系。首先，我们从几何角度研究码字重量的行为，通过相关单纯复形的组合结构对其进行解释。该方法使我们能够依据复形的特定几何特征来描述码的最小距离。随后，我们分析了单纯复形上的各种拓扑运算如何影响码的经典参数。这项研究引出了一系列几何准则的构建，使得对这些参数进行显式控制和操作成为可能。最后，作为所得结果的应用，我们运用这些几何方法在F2上构造了若干最优线性码族。借助先前建立的几何性质，我们能够精确确定这些码族的参数。