A generalization of the cylinder conjecture for divisible codes

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Kurz, Sascha ; Mattheus, Sam:
A generalization of the cylinder conjecture for divisible codes.
Bayreuth , 2020 . - 16 S.

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Abstract

We extend the original cylinder conjecture on point sets in affine three-dimensional space to the more general framework of divisible linear codes over GF(q) and their classification. Through a mix of linear programming, combinatorial techniques and computer enumeration, we investigate the structural properties of these codes. In this way, we can prove a reduction theorem for a generalization of the cylinder conjecture, show some instances where it does not hold and prove its validity for small values of q. In particular, we correct a flawed proof for the original cylinder conjecture for q=5 and present the first proof for q=7.