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Existence of self-conjugate self-orthogonal diagonal latin squares

✍ Scribed by F. E. Bennett; B. Du; H. Zhang

Publisher: John Wiley and Sons
Year: 1998
Tongue: English
Weight: 229 KB
Volume: 6
Category: Article
ISSN: 1063-8539
DOI: 10.1002/(sici)1520-6610(1998)6:1<51::aid-jcd4>3.0.co;2-v

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✦ Synopsis

In this article we give some new constructions of self-conjugate self-orthogonal diagonal Latin squares (SCSODLS). As an application of such constructions, we give a conclusive result regarding the existence of SCSODLS and show that there exists an SCSODLS of order n if and only if n ≡ 0, 1 (mod 4), except for n = 5. This result completely disproves a conjecture of Danhof,

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We shall refer to a diagonal Latin square which is orthogonal to its (3, 2, 1)-conjugate and having its (3, 2, 1)-conjugate also a diagonal Latin square as a (3, 2, 1)-conjugate orthogonal diagonal Latin square, briefly CODLS. This article investigates the spectrum of CODLS and it is found that it c