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2009 Finding and Investigating Exact Spherical Codes
Jeffrey Wang
Experiment. Math. 18(2): 249-256 (2009).

Abstract

In this paper we present the results of computer searches using a variation of an energy-minimization algorithm used by Kottwitz for finding good spherical codes. We prove that exact codes exist by representing the inner products between the vectors as algebraic numbers. For selected interesting cases, we include detailed discussion of the configurations. Of particular interest are the $20$-point code in $\mathbb{R}^6$ and the $24$-point code in $\mathbb{R}^7$, each of which is the union of two cross-polytopes in parallel hyperplanes. Finally, we catalogue all of the codes we have found.

Citation

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Jeffrey Wang. "Finding and Investigating Exact Spherical Codes." Experiment. Math. 18 (2) 249 - 256, 2009.

Information

Published: 2009
First available in Project Euclid: 25 November 2009

zbMATH: 1191.05031
MathSciNet: MR2549693

Subjects:
Primary: 05B40, 52C17

Rights: Copyright © 2009 A K Peters, Ltd.

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Vol.18 • No. 2 • 2009
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