Lengths of divisible codes with restricted column multiplicities

DOI10.3934/AMC.2023050arXiv2303.17172OpenAlexW4388763661MaRDI QIDQ6431381

Publication date: 30 March 2023

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

m a t h b b 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.

Full work available at URL: https://doi.org/10.3934/amc.2023050

Mathematics Subject Classification ID

Linear codes (general theory) (94B05) Spreads and packing problems in finite geometry (51E23) Other types of codes (94B60) Combinatorial aspects of packing and covering (05B40)