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Construction of Strongly Mutually Distinct Sudoku Tables and Solid Sudoku Cubes by Cyclotomic Cosets
A new method of constructing Sudoku tables (STs) (Sudoku Latin squares) is introduced by making use of individual vectors of cyclotomic cosets of Z n , and their Kronecker product. We show that, it is possible to construct m different STs of order m such that for every 0 ≤ u, v ≤ m - 1 the (u, v)-entry of these m STs is different. These STs could be considered as a perfect set of strongly mutually distinct (SMD) STs, which in turn are used to construct a solid Sudoku cube (SSC). As a result, a new version of SMD Sudoku puzzles under a new rule and condition is introduced that are interesting for Sudoku puzzles game designers.
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