Weight distributions of six families of 3-weight binary linear codes

02/04/2020

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by   Fei Li, et al.

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First, we correct a previous erroneous result about the exponential sum ∑_x∈F_2^eχ_1(ax^2^α+1+bx). Second, we construct several families of binary linear codes of 3-weight and determine their weight distributions based on the results of the exponential sum. Most of the codes we construct can be used in secret sharing schemes.