Uniqueness of Certain Spherical Codes
We show that there is essentially only one way of arranging 240 (resp. 196560) nonoverlapping unit spheres in R 8 (resp.R 24) so that they all touch another unit sphere Ω n , and only one way of arranging 56 (resp. 4600) spheres in R 8 (resp. R 24) so that they all touch two further, touching spheres. The following tight spherical t-designs are also unique: the 5-design in Ω7, the 7-designs in Ω8 and Ω23, and the 11-design in Ω24.
KeywordsUnit Sphere Linear Code Intersection Number Minimal Norm Distance Distribution
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