Construction of Two Classes of Minimal Binary Linear Codes from Definition Sets

Abstract

Linear codes have wide applications in many fields such as data storage, communication, cryptography, combinatorics. As a subclass of linear codes, minimal linear codes can be used to construct secret sharing schemes with good access structures. In this paper, we first construct some new classes of linear codes by selecting definition set properly. Then, the lengths, dimensions and the weight distribution of the codes are determined by investigating whether the intersections of the supports of vectors and the definition sets are empty. Results show that both wide and narrow minimal linear codes are contained in the new codes. Finally, we extend some existing results to general cases.