Employing Non-Binary Simplex Codes Over $\mathbb{F}_{p}(\mathbb{F}_{p}+v\mathbb{F}_{p})$ within Various Applications

Abstract

This article examines simplex codes categorized as types $\alpha$ and $\beta$ over $\mathbb{F}_{p}(\mathbb{F}_{p}+v\mathbb{F}_{p})$, along with exploring the $p$-array Gray representations of simplex codes of types $\alpha$ and $\beta$ over the same field. Additionally, the article investigates the covering radius of simplex codes of types $\alpha$ and $\beta$ over $\mathbb{F}_{p}(\mathbb{F}_{p}+v\mathbb{F}_{p})$. Lastly, the article delves into the construction of secret sharing schemes utilizing simplex codes over the finite field $\mathbb{F}_{p}$.