Abstract
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).
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Chen, Y., Niemenmaa, M. & Vinck, A.J.H. A general check digit system based on finite groups. Des. Codes Cryptogr. 80, 149–163 (2016). https://doi.org/10.1007/s10623-015-0072-8
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DOI: https://doi.org/10.1007/s10623-015-0072-8