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

JOURNAL OF COMBINATORIAL THEORY SERIES A

卷:116

Article

Bachoc, Christine¹  Vallentin, Frank² 

[1] Univ Bordeaux 1, Lab A2X, F-33405 Talence, France

[2] CWI, NL-1098 SJ Amsterdam, Netherlands

关键词: Linear programming;    Semidefinite programming;    Spherical codes;    Spherical designs;    Petersen graph;   

DOI  :  10.1016/j.jcta.2008.05.001

来源: Elsevier

【 摘 要 】

Linear programming bounds provide ail 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. (C) 2008 Elsevier Inc. All rights reserved.

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