Abstract
Using a strong definition of frequency hypercube, we define a strengthened form of orthogonality, called equiorthogonality, for sets of such hypercubes. We prove that the maximum possible number of mutually equiorthogonal frequency hypercubes (MEFH) of order n and dimension d based on m distinct symbols is (n-1)d/(m-1). A set of (n-1)d/(m-1) such MEFH is called a complete set. Because of the stronger conditions on the hypercubes, we can find complete sets of MEFH of all lower dimensions within any complete set of MEFH; this useful property is not shared by sets of mutually orthogonal hypercubes using the usual, weaker definition.
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Morgan, I.H. Equiorthogonal Frequency Hypercubes: Preliminary Theory. Designs, Codes and Cryptography 13, 177–185 (1998). https://doi.org/10.1023/A:1008282513875
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DOI: https://doi.org/10.1023/A:1008282513875