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<p>Two matrices are said to be non-overlapping when, regardless of the way one matrix is positioned on top of the other, the corresponding entries within the common region never coincide. In this paper, we present a new construction of fixed-dimension non-overlapping matrices, which generalizes the results due to Barcucci et al. in 2017. We analyze the asymptotic cardinality of the resulting set of matrices by generating functions. In comparison with the construction presented by Barcucci et al., the cardinality of the non-overlapping matrices yielded by our construction is significantly larger. Additionally, we also present a construction for variable-dimension non-overlapping matrices.</p>

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Constructions of two-dimensional non-overlapping codes

  • 期刊论文

  • 发表日期：

    2026年6月2日

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  • Chunyan Qin,
  • Zhizheng Zhang

摘要

Two matrices are said to be non-overlapping when, regardless of the way one matrix is positioned on top of the other, the corresponding entries within the common region never coincide. In this paper, we present a new construction of fixed-dimension non-overlapping matrices, which generalizes the results due to Barcucci et al. in 2017. We analyze the asymptotic cardinality of the resulting set of matrices by generating functions. In comparison with the construction presented by Barcucci et al., the cardinality of the non-overlapping matrices yielded by our construction is significantly larger. Additionally, we also present a construction for variable-dimension non-overlapping matrices.