On the covering structures of two classes of linear codes from perfect nonlinear functions
IEEE Transactions on Information Theory
Secret sharing schemes from binary linear codes
Information Sciences: an International Journal
SIAM Journal on Discrete Mathematics
European Journal of Combinatorics
Hi-index | 754.90 |
Secret sharing has been a subject of study for over 20 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 characterization of the minimal codewords of the underlying linear code, which is a difficult problem in general. In this paper, a sufficient condition for all nonzero codewords of a linear code to be minimal is derived from exponential sums. Some linear codes whose covering structure can be determined are constructed, and then used to construct secret sharing schemes with nice access structures.