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On Dimensionally Orthogonal Diagonal Hypercubes
Xiao-Nan LU Tomoko ADACHI
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences
Publication Date: 2020/10/01
Online ISSN: 1745-1337
Type of Manuscript: Special Section PAPER (Special Section on Discrete Mathematics and Its Applications)
Latin square, Latin cube, dimensional orthogonality, transversal, finite field, permutation polynomial, irreducible polynomial,
Full Text: FreePDF
In this paper, we propose a notion for high-dimensional generalizations of mutually orthogonal Latin squares (MOLS) and mutually orthogonal diagonal Latin squares (MODLS), called mutually dimensionally orthogonal d-cubes (MOC) and mutually dimensionally orthogonal diagonal d-cubes (MODC). Systematic constructions for MOC and MODC by using polynomials over finite fields are investigated. In particular, for 3-dimensional cubes, the results for the maximum possible number of MODC are improved by adopting the proposed construction.