A Generalization of the Cylinder Conjecture for Divisible Codes

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