Sudoku-like arrays, codes and orthogonality

M. Huggan, G. L. Mullen, B. Stevens, D. Thomson

Research output: Contribution to journalArticlepeer-review

8 Scopus citations


This paper is concerned with constructions and orthogonality of generalized Sudoku arrays of various forms. We characterize these arrays based on their constraints; for example Sudoku squares are characterized by having strip and sub-square constraints. First, we generalize Sudoku squares to be multi-dimensional arrays with strip and sub-cube constraints and construct mutually orthogonal sets of these arrays using linear polynomials. We add additional constraints motivated by elementary intervals for low discrepancy sequences and again give a construction of these arrays using linear polynomials in detail for 3 dimensional and a general construction method for arbitrary dimension. Then we give a different construction of these hypercubes due to MDS codes. We also analyze the orthogonality of all of the Sudoku-like hypercubes we consider in this paper.

Original languageEnglish (US)
Pages (from-to)675-693
Number of pages19
JournalDesigns, Codes, and Cryptography
Issue number3
StatePublished - Mar 1 2017

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science Applications
  • Discrete Mathematics and Combinatorics
  • Applied Mathematics


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