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Cyclic codes are an interesting type of linear codes and have wideapplications in communication and storage systems due to their efficientencoding and decoding algorithms. Inspired by the recent work on binary cycliccodes published in IEEE Trans. Inf. Theory, vol. 68, no. 12, pp. 7842-7849,2022, and the arXiv paper arXiv:2301.06446, the objectives of this paper arethe construction and analyses of four infinite families of ternary cyclic codeswith length $n=3^m-1$ for odd $m$ and dimension $k \in \{n/2, (n + 2)/2\}$whose minimum distances have a square-root-like lower bound. Their duals haveparameters $[n, k^\perp, d^\perp]$, where $k^\perp \in \{n/2, (n- 2)/2\}$ and$d^\perp$ also has a square-root-like lower bound. These families of codes andtheir duals contain distance-optimal cyclic codes.

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