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As a subclass of linear codes, cyclic codes have applications in consumerelectronics, data storage systems, and communication systems as they haveefficient encoding and decoding algorithms. In this paper, five families ofthree-weight ternary cyclic codes whose duals have two zeros are presented. Theweight distributions of the five families of cyclic codes are settled. Theduals of two families of the cyclic codes are optimal.

Five Families of Three-Weight Ternary Cyclic Codes and Their Duals