Two classes of new optimal ternary cyclic codes

Due to their wide applications in consumer electronics, data storage systems and communication systems, cyclic codes have been an interesting subject of study in recent years. The construction of optimal cyclic codes over finite fields is important as they have maximal minimum distance once the length and dimension are given. In this paper, we present two classes of new optimal ternary cyclic codes $ \mathcal{C}_{(2,v)} $ by using monomials $ x^2 $ and $ x^v $ for some suitable $ v $ and explain the novelty of the codes. Furthermore, the weight distribution of $ \mathcal{C}_{(2,v)}^{\perp} $ for $ v = \frac{3^{m}-1}{2}+2(3^{k}+1) $ is determined.