Several classes of two-weight and three-weight linear codes

Linear codes with few weights have been widely studied due to their applications in secret sharing, authentication codes, association schemes and strongly regular graphs. In this paper, we further construct several classes of new two-weight and three-weight linear codes from defining sets and determine their weight distributions by applications of the theory of quadratic forms and Weil sums over finite fields. Some of the linear codes obtained are optimal or almost optimal with respect to the Griesmer bound. This paper generalizes some results in~\cite{Jian2019,LiYueFu2016}.

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