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 Fqᵐ with one single maximal element, we construct four families of linear codes over the ring Fq+u Fq (u²=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 Fq, including (near) Griesmer codes and distance-optimal codes.