Strong forms of orthogonality for sets of frequency hypercubes
نویسندگان
چکیده
For frequency hypercubes of dimension d > 2, we discuss several generalizations of the usual notion of pairwise orthogonality. We provide some constructions for complete sets of orthogonal frequency hypercubes. 1. Strong orthogonality for frequency hypercubes In this paper we will examine strong forms of orthogonality for frequency hypercubes. The standard de nition requires that each ordered pair occurs the same number of times in the superimposition of two hypercubes, but this de nition says nothing about the location of the occurrences of these pairs. In [2], the authors examine several di erent forms of orthogonality which keep track of the positions of ordered pairs for orthogonal hypercubes. In this paper, we extend many of the ideas found in [2] to frequency hypercubes. In [6], the author de nes a notion of orthogonality, called equiorthogonality, which requires corresponding subarrays be either orthogonal or isomorphic. We will modify this concept and de ne more precisely which subarrays must be orthogonal and which can be isomorphic.
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