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Determination of the number of unambiguous bit matrices

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Abstract

A computationally convenient formula is derived that allows the calculation of the number of unambiguous bit matrices of orderm × n. The result shows that the compression of a large binary matrix by using unambiguous bit matrices is generally impractical unless additional information about the original matrix is available.

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References

  1. D. R. King, “The binary vector as the basis of an inverted index file,”J. Libr. Autom. 7(4):307–315 (1974).

    Google Scholar 

  2. A. Rosenfeld,Picture Processing by Computer (Academic Press, New York, 1969).

    Google Scholar 

  3. E. S. Page and L. B. Wilson,Information Representation and Manipulation in a Computer (Cambridge University Press, Cambridge, 1973).

    Google Scholar 

  4. R. S. Varga,Matrix Iterative Analysis (Prentice Hall, Englewood Cliffs, New Jersey, 1962).

    Google Scholar 

  5. H. S. Heaps and L. H. Thiel, “Optimum procedures for economic information retrieval,”Inf. Storage Retr. 6(2) (1970).

  6. H. Kobayashi and L. R. Bahl, “Image data compression by predictive coding,”IBM J. Res. Dev. 18(2) (1974).

  7. E. L. Amidon and G. S. Akin, “Algorithmic selection of the best method for compressing map data strings,”Commun. ACM 14(12) (1971).

  8. S. K. Chang, “The reconstruction of binary patterns from their projections,”Commun. ACM 14(1) (1971).

  9. S. K. Chang and G. L. Shelton, “Two algorithms for multiple view binary pattern reconstruction,”IEEE Trans. Syst., Man Cybern. 3(1) (1971).

  10. Y. R. Wang, “Data Retrieval Algorithms for Unambiguous Bit Matrices,” Paper presented at the Seventh Annual Princeton Conference on Information Science and Systems, March 22/23 (1973).

  11. L. Countet,Advanced Combinations (D. Reidal, Boston, 1974).

    Google Scholar 

  12. L. D. Davidson, “Theory of Adaptive Data Compression,” inAdvances in Communication Systems, A. V. Balakrishnan, Ed. (Academic Press, New York, 1966).

    Google Scholar 

  13. C. K. Wong and P. C. Yue, “Reconstruction of patterns by block projection,”Inf. Sci. 4:357–366 (1972).

    Google Scholar 

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The authors would like to express their thanks to the referees for their criticism and comments. The support of the National Research Council of Canada and of the University Council for Research of St. Francis Xavier University is gratefully acknowledged.

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Aalto, S., Schuegraf, E. Determination of the number of unambiguous bit matrices. International Journal of Computer and Information Sciences 6, 223–235 (1977). https://doi.org/10.1007/BF01002333

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  • DOI: https://doi.org/10.1007/BF01002333

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