On T-avoiding spherical codes and designs in ℝ³²

2025/12/28 by P. Boyvalenkov, Boyvalenkov, P., D. Cherkashin +7
Mathematics · Computer Science · #Mathematical Approximation and Integration #Coding theory and cryptography #Advanced Harmonic Analysis Research

paper · doi:10.48550/arxiv.2512.23092

Abstract

In this article, we show that the minimal vectors of the extremal even unimodular lattices in ℝ³² are T-avoiding universally optimal for suitable sets T. Moreover, they are minimal T-avoiding spherical designs and maximal T-avoiding codes for appropriate choices of T.

Citations

• Universal optimality of T-avoiding spherical codes and designs
• Energy of codes with forbidden distances in 48 dimensions
• The kissing number in 48 dimensions for codes with certain forbidden distances is 52 416 000
• Universal optimality of the E₈ and Leech lattices and interpolation formulas
• Boris Venkov's Theory of Lattices and Spherical Designs

Related

• Universal optimality of T-avoiding spherical codes and designs
• Energy of codes with forbidden distances in 48 dimensions
• The kissing number in 48 dimensions for codes with certain forbidden distances is 52 416 000
• A Note on Optimal Unimodular Lattices
• Stability of optimal spherical codes