Lengths of divisible codes with restricted column multiplicities

03/30/2023

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by   Theresa Körner, et al.

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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 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.