On Check Digit Systems Using Anti-Symmetric Mappings

  • Ralph-Hardo Schulz


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.


Detection Rate Check Equation Dihedral Group Chevalley Group Complete Mapping 
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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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