From Sidelnikov-Welch bounds to projection constants

@misc{deregowska2026from,
  title = {{From Sidelnikov-Welch bounds to projection constants}},
  author = {Beata Deregowska and Barbara Lewandowska},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.29422},
  eprint = {2609.29422},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.29422},
  note = {CC BY 4.0},
}

TY  - UNPB
TI  - From Sidelnikov-Welch bounds to projection constants
AU  - Beata Deregowska
AU  - Barbara Lewandowska
PY  - 2026
DA  - 2026/09/24
PB  - arXiv
DO  - 10.48550/arxiv.2609.29422
UR  - https://arxiv.org/abs/2609.29422
AB  - In the paper, we prove a recursive version of the weighted Sidelnikov-Welch inequality for real and complex unit vectors. Unlike the classical form, which gives a direct lower bound for a fixed even power sum, our inequality relates two consecutive even power sums. Iteration yields the usual weighted Sidelnikov-Welch bound. We apply this estimate to maximal relative projection constants. If 𝕂^m admits a maximal equiangular tight frame with M_𝕂 vectors, then for every integer k≥1, λ_𝕂(kM_𝕂−m,kM_𝕂) = λ_𝕂(m)−2m/kM_𝕂+1. Moreover, the maximal value is realized by an equiangular tight frame when k=1 and by a biangular tight frame when k≥2.
ER  -