Saturated configuration and new large construction of equiangular lines

Quasi-Equiangular Frame (QEF) : A New Flexible Configuration of Frame

Frame theory is a powerful tool in the domain of signal processing and communication. Among its numerous configurations, the ones which have drawn much attention recently are Equiangular Tight Frames(ETFs) and Grassmannian Frames. These frames both have optimality in coherence, thus bring robustness and optimal performance in applications such as digital fingerprint, erasure channels, and Compr...

New Bounds for Equiangular Lines and Spherical Two-Distance Sets

The set of points in a metric space is called an s-distance set if pairwise distances between these points admit only s distinct values. Two-distance spherical sets with the set of scalar products {α,−α}, α ∈ [0, 1), are called equiangular. The problem of determining the maximal size of s-distance sets in various spaces has a long history in mathematics. We determine a new method of bounding th...

Large Equiangular Sets of Lines in Euclidean Space

A construction is given of 29(d + 1) 2 equiangular lines in Euclidean d-space, when d = 3 · 22t−1 − 1 with t any positive integer. This compares with the well known “absolute” upper bound of 12d(d+ 1) lines in any equiangular set; it is the first known constructive lower bound of order d2 . For background and terminology we refer to Seidel [3]. The standard method for obtaining a system of equi...

Equiangular lines in Euclidean spaces

On Weyl-Heisenberg orbits of equiangular lines

An element z ∈CPd−1 is called fiducial if {gz : g ∈G} is a set of lines with only one angle between each pair, where G∼= Zd × Zd is the one-dimensional finite Weyl-Heisenberg group modulo its centre. We give a new characterization of fiducial vectors. Using this characterization, we show that the existence of almost flat fiducial vectors implies the existence of certain cyclic difference sets. ...