Five-Lee-weight linear codes over $\mathbb{F}_{q}+u\mathbb{F}_{q}$

Abstract: In this study, linear codes having their Lee-weight distributions over the semi-local ring $\mathbb{F}<em>{q}+u\mathbb{F}</em>{q}$ with $u<sup>{2}=1$ are constructed using the defining set and Gauss sums for an odd prime $q$. Moreover, we derive complete Hamming-weight enumerators for the images of the constructed linear codes under the Gray map. We finally show an application to secret sharing schemes.