Stability of optimal spherical codes

• DOI: 10.1007/s00605-024-02021-6
• Publication Date: 2024-10-07T13:02:24Z
• Authors: Károly J. Böröczky; Alexey Glazyrin
• Keywords: FOS: Computer and information sciences; Computer Science - Information Theory; Information Theory (cs.IT); 0101 mathematics; 01 natural sciences

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 general framework for showing stability such and use prove two spherical codes formed by minimal vectors lattice $$E_8$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>E</mml:mi> <mml:mn>8</mml:mn> </mml:msub> </mml:math> Leech lattice.