On projective $q^r$-divisible codes

Abstract

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.

38 pages

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Cited by in corpus (1)

• Partial spreads and vector space partitions