Secret sharing schemes have been studied for over twenty years. An important ap-proach to the construction of secret sharing schemes is based on linear codes. The access structure of the secret sharing scheme based on a linear code is determined by the minimal codewords of the dual code. However, it is very hard in general to deter-mine the minimal codewords of linear codes. Although every linear code gives rise to a secret sharing scheme, the access structure of secret sharing schemes based on only a few classes of codes are determined....[ Read more ]

Secret sharing schemes have been studied for over twenty years. An important ap-proach to the construction of secret sharing schemes is based on linear codes. The access structure of the secret sharing scheme based on a linear code is determined by the minimal codewords of the dual code. However, it is very hard in general to deter-mine the minimal codewords of linear codes. Although every linear code gives rise to a secret sharing scheme, the access structure of secret sharing schemes based on only a few classes of codes are determined.

The main contributions of this thesis are a new characterization of the minimal codewords of linear codes, the construction of several classes of linear codes that are either optimal or almost optimal, and the determination of the access structures of the secret sharing schemes based on the duals of these linear codes. The access structures of the secret sharing schemes presented in this thesis are of two types and are very nice.