A construction of unimodular equiangular tight frames from resolvable Steiner systems

An equiangular tight frame (ETF) is an M x N matrix which has orthogonal equal norm rows, equal norm columns, and the inner products of all pairs of columns have the same modulus. In this paper we study ETFs in which all of the entries are unimodular, and in particular pth roots of unity. A new construction of unimodular ETFs based on resolvable Steiner systems is presented. This construction gives many new examples of unimodular ETFs. In particular, an new infinite class of ETFs with entries in {1, -1} is presented.