Optimal linear codes with few weights from simplicial complexes

Recently, constructions of optimal linear codes from simplicial complexes have attracted much attention and some related nice works were presented. Let $q$ be a prime power. In this paper, by using the simplicial complexes of ${\mathbb{F}}_q^m$ with one single maximal element, we construct four families of linear codes over the ring ${\mathbb{F}}_q+u{\mathbb{F}}_q$ ($u^2=0$), which generalizes the results of [IEEE Trans. Inf. Theory 66(6):3657-3663, 2020]. The parameters and Lee weight distributions of these four families of codes are completely determined. Most notably, via the Gray map, we obtain several classes of optimal linear codes over ${\mathbb{F}}_q$, including (near) Griesmer codes and distance-optimal codes.