  A fascinating topic of combinatorics is $t$-designs, which have a very long
history. The incidence matrix of a $t$-design generates a linear code over
GF$(q)$ for any prime power $q$, which is called the linear code of the
$t$-design over GF$(q)$. On the other hand, some linear codes hold $t$-designs
for some $t \geq 1$. The purpose of this paper is to study the linear codes of
some $t$-designs held in the Reed-Muller and Simplex codes. Some general theory
for the linear codes of $t$-designs held in linear codes is presented. Open
problems are also presented.
