In this paper, we obtain a new explicit family of $2$-quasi-perfect Lee codes of arbitrarily large length. Our construction is based on generating sets of abelian (almost) Ramanujan graphs obtained by Forey, Fresán, Kowalski and Wigderson. Also, we develop a relationship between certain abelian Ramanujan graphs and $2$-quasi-perfect Lee codes obtained by Mesnager, Tang and Qi.

翻译：本文构造了一族新的显式任意长$2$-拟完美Lee码。我们的构造基于Forey、Fresán、Kowalski和Wigderson所获得的阿贝尔（近似）Ramanujan图的生成集。同时，我们建立了特定阿贝尔Ramanujan图与Mesnager、Tang和Qi所获$2$-拟完美Lee码之间的关联关系。