Several infinite families of binary cyclic codes with square-root-like lower bounds

Cyclic codes are important in both theory and practice and have wide applications in communication and storage systems. It is interesting to construct infinite families of binary cyclic codes, where dimensions are close to half of the length and the minimum distances approach the square-root bound. Motivated by recent works on binary cyclic codes published by Tang and Ding (2022)[9] and Liu et al. (2023) [4], the objective of this paper is to construct several infinite families of binary cyclic codes of length $ \mathrm{2^m-1} $ and dimensions close to half of the length. We developed some lower bounds on their minimum distances using the BCH bound for cyclic codes, which exhibit square-root-like lower bounds. The parameters of the dual codes of these binary cyclic codes were also investigated.