# Spherical 2-distance sets which are spherical 3-design

**Authors:**P. Boyvalenkov, M. Stoyanova

We classify spherical codes which admit exactly two different nonzero distances between their points and are spherical $3$-designs. We prove that such codes have the maximal possible cardinality provided the dimension and the minimum distance are fixed.

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**Keywords:**spherical designs, maximal spherical codes, 2-distance sets

**2000 MSC:**05B30