Lengths of divisible codes with restricted column multiplicities

Titelangaben

Körner, Theresa ; Kurz, Sascha:
Lengths of divisible codes with restricted column multiplicities.
In: Advances in Mathematics of Communications. Bd. 18 (2024) Heft 2 . - S. 505-534.
ISSN 1930-5346
DOI: https://doi.org/10.3934/amc.2023050

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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.