Line systems passing through the origin of the d-dimensional Euclidean space admitting exactly two distinct angles are called biangular. It is shown that the maximum cardinality of biangular lines is at least \(2(d-1)(d-2)\), and this result is sharp for \(d\in \{4,5,6\}\). Connections to binary codes, few-distance sets, and association schemes are explored, along with their multiangular generalization.

中文翻译：

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再谈双角线

穿过d维欧几里德空间原点并精确地允许两个不同角度的线系统称为双角线。结果表明，双角线的最大基数至少为\（2（d-1）（d-2）\），并且对于\ {d \ in \ {4,5,6 \} \ ）。探索了与二进制代码，少距离集和关联方案的连接，以及它们的多角度概括。