We propose a binary representation of categorical values using a linear map. This linear representation preserves the neighborhood structure of categorical values. In the context of evolutionary algorithms, it means that every categorical value can be reached in a single mutation. The linear representation is embedded into standard metaheuristics, applied to the problem of Sudoku puzzles, and compared to the more traditional direct binary encoding. It shows promising results in fixed-budget experiments and empirical cumulative distribution functions with high dimension instances, and also in fixed-target experiments with small dimension instances.