  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 IEEE Trans. Inf. Theory, vol. 68, no. 12, pp. 7842-7849,
2022, the objectives of this paper are the construction and analyses of five
infinite families of binary cyclic codes with parameters $[n, k]$ and $(n-6)/3
\leq k \leq 2(n+6)/3$. Three of the five families of binary cyclic codes and
their duals have a very good lower bound on their minimum distances and contain
distance-optimal codes. The other two families of binary cyclic codes are
composed of binary duadic codes with a square-root-like lower bound on their
minimum distances. As a by-product, two infinite families of self-dual binary
codes with a square-root-like lower bound on their minimum distances are
obtained.
