A Family of Five-Weight Cyclic Codes and Their Weight Enumerators

Cyclic codes are a subclass of linear codes and have applications in consumer electronics, data storage systems, and communication systems as they have efficient encoding and decoding algorithms. In this paper, a family of $p$-ary cyclic codes whose duals have three zeros are proposed. The weight distribution of this family of cyclic codes is determined. It turns out that the proposed cyclic codes have five nonzero weights.Comment: 14 Page