Sets of Complex Unit Vectors with Two Angles and Distance-Regular Graphs

We study {0,α}-sets, which are sets of unit vectors of $\mathbb{C}^m$ in which any two distinct vectors have angle 0 or α. We investigate some distance-regular graphs that provide new constructions of {0,α}-sets using a method by Godsil and Roy. We prove bounds for the sizes of {0,α}-sets of flat vectors, and characterize all the distance-regular graphs that yield {0,α}-sets meeting the bounds at equality.

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