Four infinite families of ternary cyclic codes with a square-root-like lower bound

Cyclic codes are an interesting type of linear codes and have wide applications in communication and storage systems due to their efficient encoding and decoding algorithms. Inspired by the recent work on binary cyclic codes published in Tang and Ding (2022) [26] and the works in Liu et al. (2023) [15] and Liu et al. (2023) [16], the objectives of this paper are the construction and analysis of four infinite families of ternary cyclic codes with length n=3^m−1 for odd m and dimension k∈{n/2,(n+2)/2} whose minimum distances have a square-root-like lower bound. Their duals have parameters [n,k^⊥,d^⊥], where k^⊥∈{n/2,(n−2)/2} and d^⊥ also has a square-root-like lower bound. These families of codes and their duals contain distance-optimal cyclic codes.