Two Families of Optimal Ternary Cyclic Codes With Two Zeros

Cyclic codes are an important subclass of linear codes and have wide applications in consumer electronics, data storage systems and communication systems as they have efficient encoding and decoding algorithms. In this paper, two families of optimal ternary cyclic codes with parameters [3(m) - 1, 3(m)-2 m-1, 4] are presented. The first family of cyclic codes with two zeros pi and pi(v) is constructed by using multivariate method. The second family of cyclic codes with two zeros pi(2) and pi(v) is obtained by analyzing irreducible factors of certain polynomials with finite degrees over the finite field F-3m, where pi is a generator of F-3m(*).