Stability of optimal spherical codes
K\'aroly J. B\"or\"oczky, Alexey Glazyrin
TL;DR
This paper develops a general framework to analyze the stability of optimal spherical codes and applies it to prove the stability of codes derived from the $E_8$ lattice and the Leech lattice.
Contribution
The paper introduces a new framework for stability analysis of extremal spherical codes and demonstrates its effectiveness on well-known lattice-based codes.
Findings
Stability framework applicable to extremal spherical codes.
Proved stability of $E_8$ lattice minimal vectors.
Proved stability of Leech lattice minimal vectors.
Abstract
For many extremal configurations of points on a sphere, the linear programming approach can be used to show their optimality. In this paper we establish the general framework for showing stability of such configurations and use this framework to prove the stability of the two spherical codes formed by minimal vectors of the lattice and of the Leech lattice.
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Taxonomy
TopicsMathematical Approximation and Integration · Advanced Numerical Analysis Techniques · Digital Image Processing Techniques