We prove that binary even LCD code and some graphs are in one-to-one correspondence in a certain way. Furthermore, we show that adjacency matrices of non-isomorphic simple graphs give inequivalent binary LCD codes, and vice versa.

翻译：我们证明了二元偶线性互补对偶码与某些图在一定方式下存在一一对应关系。此外，我们证明了非同构简单图的邻接矩阵生成不等价的二元线性互补对偶码，反之亦然。