Five classes of optimal two-weight linear codes

Abstract

Linear codes with few weights have applications in secret sharing, authentication codes, association schemes, data storage systems, strongly regular graphs and some other fields. Two-weight linear codes are particularly interesting since they are closely related to finite geometry, combinatorial designs, graph theory. In this paper, we propose five classes of two-Lee-weight codes over the ring $\mathbb {F}_{q}+u\mathbb {F}_{q}$ . By the Gray map, we obtain five classes of linear codes with two weights over $\mathbb {F}_{q}$ and these linear codes are optimal with respect to the Griesmer bound. As applications, we can employ these linear codes to construct secret sharing schemes with nice access structures.