Secret Sharing Schemes from Linear Codes over F2+vF2+v2F2

Abstract

Secret sharing is an important concept in cryptography, however it is a difficult problem to determine the access structure of the secret sharing scheme based on a linear code. In this work, we construct two-weight linear codes over finite field by using linear codes over finite ring. We first study MacDonald codes over the finite ring F 2 + v F 2 + v 2 F 2 with v 3 = v . Then we give torsion codes of MacDonald codes of type α and β, which are two-weight linear codes. Finally we give the access structures of secret sharing schemes based on the dual codes of the two-weight codes.