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Recently, several infinite families of minimal and optimal linear codes are obtained from simplicial complexes or down-sets by Hyun and Wu et al. Motivated by their work, we give two new constructions of codes over the ring F p + u F p , u 2 = u by using down-sets. We compute the Lee weight distributions of two classes of codes when the down-sets are generated by a single maximal element. Moreover, by using the Gray map, we obtain two classes of codes, which are minimal and distance optimal. [ABSTRACT FROM AUTHOR]

We construct an infinite family of two-Lee-weight codes over the ring F 2 + u F 2 + v F 2 + u v F 2 . These codes are defined as trace codes and have the algebraic structure of abelian codes. Their Lee weight distribution is computed by using character sums. Then, taking Gray mapping, we obtain an infinite family of abelian binary two-weight codes which are shown to be optimal by application of the Griesmer bound. Moreover, an application to secret sharing schemes is given. [ABSTRACT FROM AUTHOR]