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Boolean functions have very nice applications in cryptography and codingtheory, which have led to a lot of research focusing on their applications. Theobjective of this paper is to construct binary linear codes with few weightsfrom the defining set, which is defined by some special Boolean functions andsome additional restrictions. First, we provide two general constructions ofbinary linear codes with three or four weights from Boolean functions with atmost three Walsh transform values and determine the parameters of their dualcodes. Then many classes of binary linear codes with explicit weightenumerators are obtained. Some binary linear codes and their duals obtained areoptimal or almost optimal. The binary linear codes obtained in this paper mayhave a special interest in secret sharing schemes, association schemes,strongly regular graphs.

Binary linear codes with few weights from Boolean functions