Linear codes with few weights over $\mathbb{F}_{p}+u\mathbb{F}_{p}$ (2406.18325v1)

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.