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2021

Divisible Codes

Kurz, Sascha

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A linear code over $\mathbb{F}_q$ with the Hamming metric is called $\Delta$-divisible if the weights of all codewords are divisible by $\Delta$.

They have been introduced by Harold Ward a few decades ago.
Applications include subspace codes, partial spreads, vector space partitions, and distance optimal codes.
The determination of the possible lengths of projective divisible codes is an interesting and comprehensive challenge.

Divisible Codes · Around

Built on

At the dawn of the theory of codes
Alexander Barg · 1993
Earlier work this paper cites.
Two projective surfaces with many nodes, admitting the symmetries of the icosahedron
Wolf Paul Barth · 1996
Earlier work this paper cites.

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Cusps and codes
Wolf Paul Barth and Sławomir Rams · 2007
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Affine vector space partitions
John Bamberg, Yuval Filmus, Ferdinand Ihringer, and Sascha Kurz
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Then

Constructions and Classifications of Geometrical Structures
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Daniele Bartoli · 2012
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