  There are several methods for constructing secret sharing schemes, one of
which is based on coding theory. Theoretically, every linear code can be used
to construct secret sharing schemes. However, in general, determining the
access structures of the schemes based on linear codes is very hard. This paper
proposed the concept of minimal linear code, which makes the determination of
the access structures of the schemes based on the duals of minimal linear codes
easier. It is proved that the shortening codes of minimal linear codes are also
minimal ones. Then the conditions whether several types of irreducible cyclic
codes are minimal linear codes are presented. Furthermore, the access
structures of secret sharing schemes based on the duals of minimal linear codes
are studied, and these access structures in specific examples are obtained
through programming.
