There are several methods to construct multi-secret sharing schemes, one of which is based on coding theory. Generally, however, it is very hard to determine the minimal access structures of the schemes based on linear codes. In this paper, we first propose the concept of minimal linear codes so as to make it easier to determine the access structures of the schemes based on the duals of minimal linear codes. It is proved that the shortening codes of minimal linear codes are also minimal ones. Then we present the algorithm to determine whether a class of linear codes are minimal. On the basis of our aforementioned studies, we further devise a new multi-use multi-secret sharing scheme based on the dual code of a minimal linear code, where each participant has to carry only one share. Furthermore, we study the minimal access structures of the multi-secret sharing scheme and present specific examples through programming. Copyright © 2014 John Wiley & Sons, Ltd.