Equiangular tight frames from Paley tournaments

We prove the existence of equiangular tight frames having n = 2d - 1 elements drawn from either C-d or Cd-1 whenever n is either 2(k) - 1 for k epsilon N, or a power of a prime such that n = 3 mod 4. We also find a simple explicit expression for the prime power case by establishing a connection to a 2d-element equiangular tight frame based on quadratic residues. (c) 2007 Elsevier Inc. All rights reserved.