Lengths of divisible codes with restricted column multiplicities

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Körner, Theresa ; Kurz, Sascha:
Lengths of divisible codes with restricted column multiplicities.
Bayreuth , 2023 . - 26 S.

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Abstract

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 GF(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.