2025/09/01 by Radel Ben Av, Xuemei Chen, Av, Radel Ben +5
Computer Science · Engineering · Mathematics · #05B30 #05E18 #15B34 #22D10 #Coding theory and cryptography #Combinatorics (math.CO) #FOS: Mathematics #Mathematical Analysis and Transform Methods #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.2509.01753
openalex publication_date 2025/09/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper studies group frames (G-frames) where the unitary group representation can be projective. When the group is abelian, for most combinations N, n, we show that ETF(N,n) can only exist for genuinely projective group representations. In particular, cyclic-group frames for such parameters do not exist. We also give a characterization of all dihedral tight frames and dihedral ETF(2n,n), using which, we conclude that regular dihedral ETF(2n,n) must be genuinely projective. Following that, we give a characterization of regular dihedral ETF(2n,n) in terms of certain structured skew Hadamard matrices. We then show that Paley ETF(2n,n) and its doubling are both of this type. Finally, we classify all regular dihedral ETF(2n,n) for n≤ 22 up to switching equivalence.