Three families of binary cyclic codes with good lower bounds

Constructing an infinite family of binary cyclic codes with good parameters is an interesting topic. The objective of this paper is to construct several families of binary cyclic codes with a square-root-like lower bound. An infinite family of binary cyclic codes of length $ 2^m-1 $ and minimum distance $ d\geq \lfloor \frac{2^{m-1}}{m}\rfloor+2 $ is presented. Several infinite families of binary duadic codes with variable length and have a square-root-like lower bound are constructed. As a by-product, several families of binary self-dual codes with a square-root-like lower bound are presented. These families of binary cyclic codes contain optimal linear codes.