Codes and Expansions (CodEx) Seminar
Joey Iverson (Iowa State University):
The optimal arrangement of \(2d\) lines in \(\mathbb{C}^d\)
An equiangular tight frame of size \(d \times n\) is a special kind of matrix, and when it exists, its columns represent the optimal arrangement of \(n\) lines through the origin of \(\mathbb{C}^d\).
In this talk, we pose the “\(d \times 2d\)” conjecture: for every dimension \(d\), there exists an equiangular tight frame of size \(d \times 2d\).
Furthermore, we:
- construct two new infinite families,
- identify a third construction that conjecturally applies for all \(d\), and
- show the conjecture holds for all \(d \leq 162\).