On Dimensionally Orthogonal Diagonal Hypercubes

Xiao-Nan LU  Tomoko ADACHI  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E103-A   No.10   pp.1211-1217
Publication Date: 2020/10/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.2019DMP0009
Type of Manuscript: Special Section PAPER (Special Section on Discrete Mathematics and Its Applications)
Category: combinatorics
Latin square,  Latin cube,  dimensional orthogonality,  transversal,  finite field,  permutation polynomial,  irreducible polynomial,  

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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.