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Check character systems

Prüfzeichen-Verfahren

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Abstract

A hopefully complete review is given of different decimal codes that are in use. The grouptheoretical background of those methods is explained and applied to the construction of new error detecting codes. With the help of Latin squares (or quasi-groups) new error codes are found, especially a good decimal shift-code.

Zusammenfassung

Wir geben einen möglichst vollständigen Überblick über alle gebräuchlichen Prüfziffern-Verfahren. Der gruppentheoretische Hintergrund aller dieser Verfahren wird erklärt, und es wird gezeigt, wie sich auf dieser Basis neue Prüfzeichen-Verfahren konstruieren lassen. Mit Hilfe lateinischer Quadrate (oder Quasigruppen) werden neue Prüfzeichen-Verfahren gefunden, speziell ein guter dezimaler Shift-Code.

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References

  1. Berger-Damiani, E. R.: Eingabesicherung durch Prüfziffern. Siemens data praxis.

  2. Berger-Damiani, E. R.: Optimierung von Prüfzeichen-Verfahren. ZAMM63, 427–429 (1983).

    Google Scholar 

  3. Black, W. L.: Error detection in decimal numbers. Proc. IEEE (Lett.)60, 331–332 (1972).

    Google Scholar 

  4. Brown, D. A. H.: Some error correcting codes for certain transposition and transcription errors in decimal integers. The Computer Journal17, 9–12 (1974).

    Google Scholar 

  5. Brown, D. A. H.: Biquinary decimal error detection codes with one, two and three check digits. The Computer Journal17, 201–204 (1974).

    Google Scholar 

  6. Carvajal, R.: Modulusk check digits and the chromatic number problem. Inf. Proc.74, 521–523 (1974).

    Google Scholar 

  7. Dénes, J., Keedwell, A. D.: Latin Squares and their Applications. New York: Academic Press 1974.

    Google Scholar 

  8. Eberlein, G.: Die automatische Nummernprüfung. Handbuch der maschinellen Datenverarbeitung,Vol. 1/4/3 (1965).

  9. Hall, M.: A combinatorial problem on abelian groups. Proc. Amer. Math. Soc.4, 912–916 (1953).

    Google Scholar 

  10. Hall, M., Paige, L. J.: Complete mappings of finite groups. Pacific J. Math.5, 541–549 (1955).

    Google Scholar 

  11. Legind Larsen, H.: Generalized double modulus 11 check digit error detection. BIT23, 303–307 (1983).

    Google Scholar 

  12. Niederreiter, H., Robinson, K. H.: Complete mappings of finite fields. J. Austral. Math. Soc. (Ser. A)33, 197–212 (1982).

    Google Scholar 

  13. Paige, L. J.: A note on finite abelian groups. Bull. Amer. Math. Soc.53 (2), 590–593 (1947).

    Google Scholar 

  14. Paige, L. J.: Complete mappings of finite groups. Pacific J. Math.1, 111–116 (1951).

    Google Scholar 

  15. Sethi, A. S., Rajaraman, V., Kenjale, P. S.: An error-correcting coding scheme for alphanumeric data. Inf. Proc. Letters7, 72–77 (1978).

    Google Scholar 

  16. Siemon, H.: Anwendungen der elementaren Gruppentheorie in Zahlentheorie und Kombinatorik. Stuttgart: Klett-Verlag 1981.

    Google Scholar 

  17. Tang, D. T., Lum, V. Y.: Error control for terminals with human operators. IBM J. Res. & Dev.14, 409–416 (1970).

    Google Scholar 

  18. Verhoeff, J.: Error detecting decimal codes. Mathematical Centre Tracts 29. Mathematisch Centrum Amsterdam, 1969.

  19. Wild, W. G.: Theory of modulosN check digit systems. Computer Bulletin12, 309–311 (1968).

    Google Scholar 

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Authors and Affiliations

  1. Bereich Datenverarbeitung und Elektronik, Hahn-Meitner-Institut Berlin GmbH., Glienicker Strasse 100, D-1000, Berlin 39

    A. Ecker

  2. WE Medizinische Informatik, Freie Universität Berlin, Hindenburgdamm 30, D-1000, Berlin 45

    G. Poch

Authors
  1. A. Ecker
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  2. G. Poch
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Ecker, A., Poch, G. Check character systems. Computing 37, 277–301 (1986). https://doi.org/10.1007/BF02251088

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  • DOI: https://doi.org/10.1007/BF02251088

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