2020/03/09 by Jonathan Jedwab, Jedwab, Jonathan, Tabriz Popatia +1 · 1 citation
Computer Science · Engineering · #Cellular Automata and Applications #Combinatorics (math.CO) #FOS: Mathematics #VLSI and FPGA Design Techniques #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.2003.03920
openalex publication_date 2020/03/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Mutually orthogonal frequency squares (MOFS) of type F(mλ;λ) generalize the structure of mutually orthogonal Latin squares: rather than each of m symbols appearing exactly once in each row and in each column of each square, the repetition number is λ≥ 1. A classical upper bound for the number of such MOFS is ((mλ-1)2)/(m-1). We introduce a new representation of MOFS of type F(mλ;λ), as a linear combination of \0,1\ arrays. We use this representation to give an elementary proof of the classical upper bound, together with a structural constraint on a set of MOFS achieving the upper bound. We then use this representation to establish a maximality criterion for a set of MOFS of type F(mλ;λ) when m is even and λ is odd, which simplifies and extends a previous analysis [T. Britz, N.J. Cavenagh, A. Mammoliti, I.M. Wanless, Mutually orthogonal binary frequency squares, Electron. J. Combin., 27(#P3.7), 2020, 26 pages] of the case when m=2 and λ is odd.