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On Check Digit Systems Using Anti-Symmetric Mappings

  • Ralph-Hardo Schulz
Chapter

Abstract

We consider check digit systems over a group G with check equation T(a 1)T 2(a 2)... T n (a n ) = e (for codewords a l a 2... a n G n ) with eG and permutation T of G. Such a system detects all single errors (i.e. errors in only one component); and it detects adjacent transpositions (i.e. errors of the form ... ab... → ... ba...) if T is anti-symmetric that means that T fulfills the condition x T(y) ≠ y T(x) for all x, yG with xy. In this survey we shall report on the existence of groups with anti-symmetric mappings, define equivalence relations between check digit systems and describe, in the special case of the dihedral group D 5, the equivalence classes.

Keywords

Detection Rate Check Equation Dihedral Group Chevalley Group Complete Mapping 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 2000

Authors and Affiliations

  • Ralph-Hardo Schulz
    • 1
  1. 1.FB Mathematik und InformatikFreie Universität BerlinBerlinGermany

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