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arXiv · 0708.3947

Optimality and uniqueness of the (4,10,1/6) spherical code

Christine Bachoc·Frank Vallentin
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Abstract

Linear programming bounds provide an elegant method to prove optimality and uniqueness of an (n,N,t) spherical code. However, this method does not apply to the parameters (4,10,1/6). We use semidefinite programming bounds instead to show that the Petersen code, which consists of the midpoints of the edges of the regular simplex in dimension 4, is the unique (4,10,1/6) spherical code.

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Christine Bachoc, Frank Vallentin. 2008-05-14. Optimality and uniqueness of the (4,10,1/6) spherical code. https://doi.org/10.1016/j.jcta.2008.05.001

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