Three Classes of Optimal Ternary Cyclic Codes and the Weight Distributions of Their Duals

Cyclic codes as a subclass of linear codes have wide applications in communication systems, consumer electronics and data storage systems, due to their efficient encoding and decoding algorithms. We construct three classes of optimal ternary cyclic codes, which meet some certain bound. The weight distributions of their duals are also completely determined. The results show that their duals have few nonzero weights.