Finite fields
How to Build Robust Shared Control Systems
Designs, Codes and Cryptography
On sharing secrets and Reed-Solomon codes
Communications of the ACM
Communications of the ACM
Variations on Minimal Codewords in Linear Codes
AAECC-11 Proceedings of the 11th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
The access structure of some secret-sharing schemes
ACISP '96 Proceedings of the First Australasian Conference on Information Security and Privacy
Minimal vectors in linear codes
IEEE Transactions on Information Theory
Secret Sharing Schemes with Nice Access Structures
Fundamenta Informaticae - SPECIAL ISSUE ON TRAJECTORIES OF LANGUAGE THEORY Dedicated to the memory of Alexandru Mateescu
Secret sharing schemes from binary linear codes
Information Sciences: an International Journal
Secret Sharing Schemes with Nice Access Structures
Fundamenta Informaticae - SPECIAL ISSUE ON TRAJECTORIES OF LANGUAGE THEORY Dedicated to the memory of Alexandru Mateescu
Secret sharing schemes based on graphical codes
Cryptography and Communications
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Secret sharing has been a subject of study for over twenty years, and has had a number of real-world applications. There are several approaches to the construction of secret sharing schemes. One of them is based on coding theory. In principle, every linear code can be used to construct secret sharing schemes. But determining the access structure is very hard as this requires the complete characterisation of the minimal codewords of the underlying linear code, which is a difficult problem. In this paper we present a sufficient condition under which we are able to determine all the minimal codewords of certain linear codes. The condition is derived using exponential sums. We then construct some linear codes whose covering structure can be determined, and use them to construct secret sharing schemes with interesting access structures.