On projective $q^r$-divisible codes

A projective linear code over $mathbb{F}_q$ is called $Delta$-divisible if all weights of its codewords are divisible by $Delta$. Especially, $q^r$-divisible projective linear codes, where $r$ is some integer, arise in many applications of collections of subspaces in $mathbb{F}_q^v$. One example are upper bounds on the cardinality of partial spreads. Here we survey the known results on the possible lengths of projective $q^r$-divisible linear codes.