Finite two-distance tight frames

Alexander Barg, Alexey Glazyrin, Kasso A. Okoudjou, Wei Hsuan Yu

Research output: Contribution to journalArticlepeer-review

31 Scopus citations

Abstract

A finite collection of unit vectors S ⊂ ℝn is called a spherical two-distance set if there are two numbers a and b such that the inner products of distinct vectors from S are either a or b. We prove that if a ≠ -b, then a two-distance set that forms a tight frame for ℝn is a spherical embedding of a strongly regular graph. We also describe all two-distance tight frames obtained from a given graph. Together with an earlier work by S. Waldron (2009) [22] on the equiangular case, this completely characterizes two-distance tight frames. As an intermediate result, we obtain a classification of all two-distance 2-designs.

Original languageEnglish
Article number13109
Pages (from-to)163-175
Number of pages13
JournalLinear Algebra and Its Applications
Volume475
DOIs
StatePublished - Jun 2015

Keywords

  • Finite tight frames
  • Spherical 2-designs
  • Spherical designs of harmonic index 2
  • Spherical two-distance sets
  • Strongly regular graphs

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