Abstract
We consider the two-dimensional generalizations of de Bruijn sequences; i.e., the integer-valued arrays whose all fragments of a fixed size (windows) are different. For these arrays, dubbed sub-de Bruijn, we consider the complexity of decoding; i.e., the determination of a position of a window with given content in an array. We propose a construction of arrays of arbitrary size with arbitrary windows where the number of different elements in the array is of an optimal order and the complexity of decoding a window is linear.
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Acknowledgments
A. D. Yashunsky expresses his gratitude to V. D. Yashunsky for drawing the author’s attention to the problem of constructing de Bruijn arrays.
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Russian Text © The Author(s), 2019, published in Diskretnyi Analiz i Issledovanie Operatsii, 2019, Vol. 26, No. 2, pp. 98–114.
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Makarov, D.A., Yashunsky, A.D. On a Construction of Easily Decodable Sub-de Bruijn Arrays. J. Appl. Ind. Math. 13, 280–289 (2019). https://doi.org/10.1134/S1990478919020091
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DOI: https://doi.org/10.1134/S1990478919020091