  Cyclic codes are the most studied subclass of linear codes and widely used in
data storage and communication systems. Many cyclic codes have optimal
parameters or the best parameters known. They are divided into simple-root
cyclic codes and repeated-root cyclic codes. Although there are a huge number
of references on cyclic codes, few of them are on repeated-root cyclic codes.
Hence, repeated-root cyclic codes are rarely studied. There are a few families
of distance-optimal repeated-root binary and $p$-ary cyclic codes for odd prime
$p$ in the literature. However, it is open whether there exists an infinite
family of distance-optimal repeated-root cyclic codes over $\bF_q$ for each
even $q \geq 4$.
  In this paper, three infinite families of distance-optimal repeated-root
cyclic codes with minimum distance 3 or 4 are constructed; two other infinite
families of repeated-root cyclic codes with minimum distance 3 or 4 are
developed; seven infinite families of repeated-root cyclic codes with minimum
distance 6 or 8 or 10 are presented; and two infinite families of repeated-root
binary cyclic codes with parameters $[2n, k, d \geq (n-1)/\log_2 n]$, where
$n=2^m-1$ and $k \geq n$, are constructed. In addition, 27 repeated-root cyclic
codes of length up to $254$ over $\bF_q$ for $q \in \{2, 4, 8\}$ with optimal
parameters or best parameters known are obtained in this paper. The results of
this paper show that repeated-root cyclic codes could be very attractive and
are worth of further investigation.
