Linear codes with few weights over ${\mathbb{F}}_p+u{\mathbb{F}}_p$

Abstract

For any positive integer $m$ and an odd prime $p$; let ${\mathbb{F}}_q+u{\mathbb{F}}_q$, where $q=p^m$, be a ring extension of the ring ${\mathbb{F}}_p+u{\mathbb{F}}_p.$ In this paper, we construct linear codes over ${\mathbb{F}}_p+u{\mathbb{F}}_p$ by using trace function defined on ${\mathbb{F}}_q+u{\mathbb{F}}_q$ and determine their Hamming weight distributions by employing symplectic-weight distributions of their Gray images.