Linear codes with few weights have applications in secret sharing, authentication codes, association schemes and strongly regular graphs. In this paper, several classes of two-weight and three-weight linear codes are presented and their weight distributions are determined using Weil sums. Some of the linear codes obtained are optimal or almost optimal with respect to the Griesmer bound.

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In this paper, several nonexistence results on generalized bent functions f : Z n 2 → Z m are presented by using the knowledge on cyclotomic number fields and their imaginary quadratic subfields.

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