Abstract
We discuss sets of mutually orthogonal frequency Sudoku squares. In particular, we provide upper bounds for the maximum number of such mutually orthogonal squares. In addition, we provide constructions for sets of such squares. We also briefly discuss an extension of these ideas to sets of higher dimensional mutually orthogonal frequency hypercubes.
This is a preview of subscription content, log in via an institution to check access.
We’re sorry, something doesn't seem to be working properly.
Please try refreshing the page. If that doesn't work, please contact support so we can address the problem.
References
Bailey R.A., Cameron P.J., Connelly R.: Sudoku, gerechte designs, resolutions, affine space, spreads, reguli, and Hamming codes. Am. Math. Mon. 115, 383–404 (2008).
Bremigan R., Lorch J.: Mutually orthogonal rectangular gerechte designs. Linear Algebra Appl. 497, 44–61 (2016).
Colbourn C.J., Dinitz J.H. (eds.): Handbook of Combinatorial Designs, 2nd edn. CRC Press, Boca Raton (2007).
Dénes J., Keedwell A.D.: Latin Squares and Their Applications. Academic Press, New York (1974).
D’haeseleer J., Metsch K., Storme L., Van de Voorde G.: On the maximality of a set of mutually orthogonal Sudoku latin squares. Des. Codes Cryptogr. 84, 143–152 (2017).
Laywine C.F., Mullen G.L.: Discrete Mathematics Using Latin Squares. Wiley, New York (1998).
Lidl R., Niederreiter H.: Finite Fields, Encyclopedia of Mathematics and Its Applications, 2nd edn. Cambridge University Press, Cambridge (1997).
Mullen G.L.: Polynomial representation of complete sets of frequency squares of prime power order. Discret. Math. 69, 79–84 (1988).
Pederson R., Vis T.: Sets of mutually orthogonal Sudoku Latin Squares. Coll. Math. J. 40(3), 174–180 (2009).
Street A.P., Street D.J.: Combinatorics of Experimental Design. Oxford University Press, New York (1987).
Acknowledgements
The authors would like to thank the referees for their helpful comments.
Author information
Authors and Affiliations
Corresponding author
Additional information
Communicated by D. Ghinelli.
Rights and permissions
About this article
Cite this article
Ethier, J.T., Mullen, G.L. Sets of mutually orthogonal Sudoku frequency squares. Des. Codes Cryptogr. 87, 57–65 (2019). https://doi.org/10.1007/s10623-018-0487-0
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10623-018-0487-0