Note on Support Weight Distribution of Linear Codes over $\mathbb{F}_{p}+u\mathbb{F}_{p}+v\mathbb{F}_{p}+uv\mathbb{F}_{p}$
Minjia Shi, Jie Tang, Maorong Ge · IEICE Transactions on Fundamentals of Electronics Communications and Computer Sciences · 2017
Let $R$ = $\mathbb{F}_{p}+u\mathbb{F}_{p}+v\mathbb{F}_{p}+uv\mathbb{F}_{p}$, where u2=u, v2 and uv=vu. A relation between the support weight distribution of a linear code $\mathscr{C}$ of type p4k over R and its dual code $\mathscr{C}^{\bot}$ is established.