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We determine the minimum possible column multiplicity of even, doubly-, andtriply-even codes given their length. This refines a classification result forthe possible lengths of $q^r$-divisible codes over $\mathbb{F}_q$. We also givea few computational results for field sizes $q>2$. Non-existence results ofdivisible codes with restricted column multiplicities for a given length haveapplications e.g. in Galois geometry and can be used for upper bounds on themaximum cardinality of subspace codes.

Lengths of divisible codes with restricted column multiplicities