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Designs, Codes and Cryptography
Published in: Designs, Codes and Cryptography 1/2016

01-07-2016

A general check digit system based on finite groups

Authors: Yanling Chen, Markku Niemenmaa, A. J. Han Vinck

Published in: Designs, Codes and Cryptography | Issue 1/2016

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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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Metadata
Title
A general check digit system based on finite groups
Authors
Yanling Chen
Markku Niemenmaa
A. J. Han Vinck
Publication date
01-07-2016
Publisher
Springer US
Published in
Designs, Codes and Cryptography / Issue 1/2016
Print ISSN: 0925-1022
Electronic ISSN: 1573-7586
DOI
https://doi.org/10.1007/s10623-015-0072-8

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