  Steiner systems are a fascinating topic of combinatorics. The most studied
Steiner systems are $S(2, 3, v)$ (Steiner triple systems), $S(3, 4, v)$
(Steiner quadruple systems), and $S(2, 4, v)$. There are a few infinite
families of Steiner systems $S(2, 4, v)$ in the literature. The objective of
this paper is to present an infinite family of Steiner systems $S(2, 4, 2^m)$
for all $m \equiv 2 \pmod{4} \geq 6$ from cyclic codes. This may be the first
coding-theoretic construction of an infinite family of Steiner systems $S(2, 4,
v)$. As a by-product, many infinite families of $2$-designs are also reported
in this paper.
