In this paper, for an odd prime p, by extending the work of Zhu et al. [22], we construct two new classes of four-weight and six-weight codes over \(\mathbb {F}_p\) from different defining sets. Moreover, we give some examples to verify our results. In some cases, there are several almost optimal codes with respect to the Griesmer bound according to the online code table [6]. Furthermore, the codes proposed have a higher rate compared with other codes, which leads to essential applications in data storage systems and association schemes.
