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Rationality of the inner products of spherical s-distance t-designs for t ≥ 2s − 2, s ≥ 3

Boyvalenkov, P ; Sharif University of Technology | 2022

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  1. Type of Document: Article
  2. DOI: 10.1016/j.laa.2022.03.028
  3. Publisher: Elsevier Inc , 2022
  4. Abstract:
  5. We prove that the inner products of spherical s-distance t-designs with t≥2s−2 (Delsarte codes) and s≥3 are rational with the only exception being the icosahedron. In other formulations, we prove that all sharp configurations have rational inner products and all spherical codes which attain the Levenshtein bound, have rational inner products, except for the icosahedron. © 2022 Elsevier Inc
  6. Keywords:
  7. S-distance sets ; Spherical codes and designs ; Codes (symbols) ; Inner product ; S-distance sets ; Spherical codes ; Spherical designs ; T-designs ; Spheres
  8. Source: Linear Algebra and Its Applications ; Volume 646 , 2022 , Pages 107-118 ; 00243795 (ISSN)
  9. URL: https://www.sciencedirect.com/science/article/abs/pii/S0024379522001367