Linear codes with a few weights are of importance in consumer electronics, communications and data storage systems, and they have many applications in secret sharing schemes, authentication codes, association schemes and strongly regular graphs. In this paper, by applying the defining set theory, a class of four-weight linear codes over F_p are constructed. Then, we use exponential sums to determine their weight distributions explicitly. Furthermore, An example is given to show the correctness of the results by Magma program.
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