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 Fq 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.
Translated title of the contribution | Een veralgemening van de cilinderconjectuur voor deelbare codes |
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Original language | English |
Pages (from-to) | 2281-2289 |
Number of pages | 9 |
Journal | IEEE Transactions on Information Theory |
Volume | 68 |
Issue number | 4 |
Early online date | 9 Dec 2021 |
DOIs | |
Publication status | Published - Apr 2022 |