Equiorthogonal Frequency Hypercubes: Preliminary Theory

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.

Department(s)

Mathematics and Statistics

Keywords and Phrases

orthogonality; frequency hypercubes; frequency squares; latin hypercubes; latin squares; orthogonal arrays

Document Type

Article - Journal

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 1998 Springer Verlag, All rights reserved.

Publication Date

01 Jan 1998

Link to Full Text

Share

 
COinS