Journal article

Publication year: 2017

Pages: 143-152

Journal: Designs, Codes and Cryptography

Volume number: 84

Issue number: 1-2

ISSN: 0925-1022

eISSN: 1573-7586

DOI Link: https://doi.org/10.1007/s10623-016-0234-3

Publisher: Springer

Abstract: 
The maximum number of mutually orthogonal Sudoku Latin squares (MOSLS) of order is n = m(2) is n - m. In this paper, we construct for n = q(2), q a prime power, a set of q(2) - q - 1 MOSLS of order q(2) that cannot be extended to a set of q(2) - q MOSLS. This contrasts to the theory of ordinary Latin squares of order n, where each set of n - 2 mutually orthogonal Latin Squares (MOLS) can be extended to a set of n - 1 MOLS (which is best possible). For this proof, we construct a particular maximal partial spread of size q(2) - q + 1 in PG(3,q) and use a connection between Sudoku Latin squares and projective geometry, established by Bailey, Cameron and Connelly.

Harvard Citation style: D'haeseleer, J., Metsch, K., Storme, L. and Van de Voorde, G. (2017) On the maximality of a set of mutually orthogonal Sudoku Latin Squares, Designs, Codes and Cryptography, 84(1-2), pp. 143-152. https://doi.org/10.1007/s10623-016-0234-3

APA Citation style: D'haeseleer, J., Metsch, K., Storme, L., & Van de Voorde, G. (2017). On the maximality of a set of mutually orthogonal Sudoku Latin Squares. Designs, Codes and Cryptography. 84(1-2), 143-152. https://doi.org/10.1007/s10623-016-0234-3