Some codes over \({\mathcal {R}}={\mathcal {R}}_{1}{\mathcal {R}}_{2}{\mathcal {R}}_{3} \) and their applications in secret sharing schemes

Abstract

Simplex and MacDonald codes have received significant attention from researchers since the inception of coding theory. In this work, we present the construction of linear torsion codes for simplex and MacDonald codes over the ring \({\mathcal {R}}={\mathcal {R}}_{1}{\mathcal {R}}_{2}{\mathcal {R}}_{3}\). We have introduced a novel family of linear codes over \({\mathbb {F}}_{p}\). These codes have been extensively examined with respect to their properties, such as code minimality, weight distribution, and their applications in secret sharing schemes. In addition to this investigation, we have discovered that these codes are also applicable to the association schemes of linear torsion codes for simplex and MacDonald codes over. \({\mathcal {R}}={\mathcal {R}}_{1}{\mathcal {R}}_{2}{\mathcal {R}}_{3}\).