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arXiv · 1912.10147

On projective $q^r$-divisible codes

Daniel Heinlein·Thomas Honold·Michael Kiermaier·Sascha Kurz·Alfred Wassermann
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Abstract

A projective linear code over $\mathbb{F}_q$ is called $Δ$-divisible if all weights of its codewords are divisible by $Δ$. 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.

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Daniel Heinlein, Thomas Honold, Michael Kiermaier, Sascha Kurz, Alfred Wassermann. 2019-12-20. On projective $q^r$-divisible codes. https://arxiv.org/abs/1912.10147

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