Working paper Open Access

# A New Checksum Formula for Error Detecting Decimal Codes

Alper, Mert Bora

##### Thesis supervisor(s)

Gandhi, Vivek

Abstract

Decimal codes are used everywhere in modern societies to identify things such as credit cards, books, and even human beings through passport numbers. All these integers are subject to various transmission errors, due to machine, and mostly human errors. Hence various error detection algorithms have been developed to mitigate the issue, even if not completely solve it through error correction.

This essay addresses the problem of detecting transmission errors in decimal codes using a single decimal checksum digit. The aim is to develop a new algorithm that can detect most of the transmission errors while being flexible at the same time so that it can be adapted to different situations. The scope of the transmission errors are limited to the 6 most common transmission errors, which constitutes 91.4% of all transmission errors, according to the Kirtland's investigation. For the scope of this paper, the new error detection algorithm is expected to deal with situations where only one transmission error occurs at a time.

In the development of The New Algorithm, a mathematical model of the problem domain is created using arrays, and afterwards, the conditions which the modelling arrays must satisfy for detecting errors are identified under the concept of The Ideal Algorithm. Afterwards, each of the modelling conditions is assigned a score depending on how "detrimental" their violation will be (which is based on the frequency of the error the condition is interested in), which in turn allowed computer assisted brute-force method to be used to find the most suitable arrays for The New Algorithm.

The New Algorithm can detect 91.05% of all transmission errors and yet, thanks to the mathematical modelling, it can be adapted to different situations in future and different local contexts.

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• H. Michael Damm. Totally anti-symmetric quasigroups for all orders n ≠ 2,6. Discrete Mathematics , 307(6):715 – 729, 2007.

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• Jacobus Verhoeff. Error detecting decimal codes. (mathematical centre tracts, 29). ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, 51(3):240–241, 1971.

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