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

References in corpus (4)

• New upper bounds for kissing numbers from semidefinite programming
• Projective divisible binary codes
• LinCode -- computer classification of linear codes
• Classification of linear codes using canonical augmentation