Designs, Codes and Cryptography

, Volume 80, Issue 1, pp 149–163 | Cite as

A general check digit system based on finite groups

  • Yanling Chen
  • Markku Niemenmaa
  • A. J. Han Vinck


In this paper, we review a new method for the universal design of a check digit system over an abelian group of arbitrary order. Furthermore, we challenge the current standards by comparing this system with several well-known and widely used systems such as ISBN, MEID, ISAN and the system over alphanumeric characters. We show that this novel design outperforms all of them in terms of the error detection capability with a comparable computational complexity. In particular, besides the well-known five types of errors to be detected (i.e., single error and four double errors which are adjacent/jump transposition and adjacent/jump twin errors), we address the \(t\)-jump transpositions and \(t\)-jump twin errors which generalize the four types of double errors, and aim to design the check digit system with a detection radius as long as possible that depends on \(t\) and reflects the capability of detecting these two special kinds of double errors. The results of this paper are based on the results of the article by Chen et al. (On some properties of a check digit system, 2012).


Abelian group Field Check digit Error detection 

Mathematics Subject Classification

20K01 11D88 94B05 


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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  • Yanling Chen
    • 1
  • Markku Niemenmaa
    • 2
  • A. J. Han Vinck
    • 3
  1. 1.Institute of Digital Communication SystemsRuhr University BochumBochumGermany
  2. 2.Department of Mathematical SciencesUniversity of OuluOuluFinland
  3. 3.Institute of Digital Signal ProcessingUniversity of Duisburg-EssenDuisburgGermany

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