Abstract
This paper presents a new approach to construct a smalln-column 0, 1-matrix for two given integersn andk(k<n), such that everyk-column projection contains all 2k possible row vectors, namely surjective on {0, 1}k. The number of the matrix's rows does not exceed\(2^k \left\lceil {\log (k^2 + 4)} \right\rceil ^{k - 1} \left( {\frac{{2 log n}}{{log(0.25k^2 + 1)}}} \right)^{\left\lceil {\log (0.25k^2 + 1)} \right\rceil } \). This approach has considerable advantage for smallk and practical sizes ofn. It can be applied to the test generation of VLSI circuits, the design of fault tolerant systems and other fields.
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Wu, H. Onn-column 0, 1-matrices with allk-projections surjective. Acta Informatica 31, 285–299 (1994). https://doi.org/10.1007/BF01218407
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DOI: https://doi.org/10.1007/BF01218407