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 e ∈ G 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, y ∈ G with x ≠ y. 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.
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Schulz, RH. (2000). On Check Digit Systems Using Anti-Symmetric Mappings. In: Althöfer, I., et al. Numbers, Information and Complexity. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-6048-4_24
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DOI: https://doi.org/10.1007/978-1-4757-6048-4_24
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