On Dimensionally Orthogonal Diagonal Hypercubes

• LU Xiao-Nan

  Department of Industrial Administration, Faculty of Science and Technology, Tokyo University of Science

• ADACHI Tomoko

  Department of Information Sciences, Toho University

Abstract

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.

Journal

• IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences

  IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences E103.A (10), 1211-1217, 2020-10-01

  The Institute of Electronics, Information and Communication Engineers

Keywords

• Latin square
• Latin cube
• dimensional orthogonality
• transversal
• finite field
• permutation polynomial
• irreducible polynomial

Details

• CRID: 1390004222629955200
• NII Article ID: 130007920249
• DOI: 10.1587/transfun.2019dmp0009
• ISSN: 17451337
• ISSN: 09168508
• Web Site: https://www.jstage.jst.go.jp/article/transfun/E103.A/10/E103.A_2019DMP0009/_pdf
• Text Lang: en
• Data Source:
  • JaLC
  • Crossref
  • CiNii Articles
  • KAKEN
• Abstract License Flag: Disallowed