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|
|Number of pages||9|
|Journal||IEEE Transactions on Information Theory|
|Early online date||9 Dec 2021|
|Publication status||Published - Apr 2022|