Lengths of divisible codes with restricted column multiplicities
Theresa Körnerm, Sascha Kurz · Advances in Mathematics of Communications · 2023
We determine the minimum possible column multiplicity of even, doubly-, and triply-even codes given their length. This refines a classification result for the possible lengths of $ q^r $-divisible codes over $ \mathbb{F}_q $. We also give a few computational results for field sizes $ q>2 $. Non-existence results of divisible codes with restricted column multiplicities for a given length have applications e.g. in Galois geometry and can be used for upper bounds on the maximum cardinality of subspace codes.