Several classes of minimal linear codes with few weights from weakly\n regular plateaued functions

Abstract

Minimal linear codes have significant applications in secret sharing schemes\nand secure two-party computation. There are several methods to construct linear\ncodes, one of which is based on functions over finite fields. Recently, many\nconstruction methods of linear codes based on functions have been proposed in\nthe literature. In this paper, we generalize the recent construction methods\ngiven by Tang et al. in [IEEE Transactions on Information Theory, 62(3),\n1166-1176, 2016] to weakly regular plateaued functions over finite fields of\nodd characteristic. We first construct three weight linear codes from weakly\nregular plateaued functions based on the second generic construction and\ndetermine their weight distributions. We next give a subcode with two or three\nweights of each constructed code as well as its parameter. We finally show that\nthe constructed codes in this paper are minimal, which confirms that the secret\nsharing schemes based on their dual codes have the nice access structures.\n