  Sum-rank codes have known applications in the multishot network coding, the
distributed storage and the construction of space-time codes. U.
Mart\'{\i}nez-Pe\~{n}as introduced the cyclic-skew-cyclic sum-rank codes and
proposed the BCH bound on the cyclic-skew-cyclic sum-rank codes in his paper
published in IEEE Trans. Inf. Theory, vol. 67, no. 8, 2021. Afterwards, many
sum-rank BCH codes with lower bounds on their dimensions and minimum sum-rank
distances were constructed. Sum-rank Hartmann-Tzeng bound and sum-rank Roos
bound on cyclic-skew-cyclic codes were proposed and proved by G. N. Alfarano,
F. J. Lobillo, A. Neri, and A. Wachter-Zeh in 2022. In this paper, cyclic,
negacyclic and constacyclic sum-rank codes are introduced and a direct
construction of cyclic, negacyclic and constacyclic sum-rank codes of the
matrix size $m \times m$ from cyclic, negacyclic and constacyclic codes over
${\bf F}_{q^m}$ in the Hamming metric is proposed. The cyclic-skew-cylic
sum-rank codes are special cyclic sum-rank codes. In addition, BCH and
Hartmann-Tzeng bounds for a type of cyclic sum-rank codes are developed.
Specific constructions of cyclic, negacyclic and constacyclic sum-rank codes
with known dimensions and controllable minimum sum-rank distances are proposed.
Moreover, many distance-optimal binary sum-rank codes and an infinite family of
distance-optimal binary cyclic sum-rank codes with minimum sum-rank distance
four are constructed. This is the first infinite family of distance-optimal
sum-rank codes with minimum sum-rank distance four in the literature.
