可除码柱面猜想的推广
A generalization of the cylinder conjecture for divisible codes
摘要：
本文将三维仿射空间中点集上的圆柱猜想推广到$\mathbb{F}_q$上的可除线性码及其分类的更一般的框架。通过混合的线性规划，组合技术和计算机枚举，我们调查这些代码的结构特性。这样，我们可以证明一个简化定理的推广的圆柱猜想，显示一些情况下，它不成立，并证明其有效性的小值的$q$。特别地，我们修正了$q = 5$原圆柱猜想的一个有缺陷的证明，并给出了$q = 7$的第一个证明.
英文摘要：
We extend the original cylinder conjecture on point sets in affine three-dimensional space to the more general framework of divisible linear codes over $\mathbb{F}_q$ 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 $q = 7$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
