Barcodes

Jacobus (Koos) Verhoeff, the Dutch mathematician who was responsible for the elegant system of designing a decimal code check digit system based on the dihedral group of order 10, was born in 1927. He studied mathematics in Leiden and Amsterdam and wrote his doctoral dissertation in the area of coding theory. In fact, the publication in which his check digit system is included was a reworked version of his thesis. He had a very varied career. He worked at the mathematics research center in Amsterdam known as the Mathematical Centre (now the Center for Mathematics and Computer Science) and taught at the Technological University in Delft. Later he worked in industry at Philips in Eindhoven. Finally, he became a full professor of Computer Science at Erasmus University in Rotterdam. He is now retired.

Not only did Verhoeff develop a system of detecting errors in a decimal digit code environment but he also error correction systems as well. This work is less well known because it was published in Dutch. In addition to his work work on error detection and correction codes, and other work in coding theory, Verhoeff was a pioneer in work involved in the design of library information retrieval systems (see References, below).

Besides his career as a mathematician, Jacobus Verhoeff also produces art, more specifically sculpture, which is inspired by mathematics. Some of his fascinating work has appeared in various shows.

I am indebted to Tom Verhoeff, son of Koos, for most of the information here. Tom Verhoeff is a mathematical computer scientist.

**References:**

Verhoeff, J., Error Detecting Decimal Codes, Mathematical Centre, Amsterdam, 1969.

Verhoeff, J., Wiskundige aspecten van het Nederlandse administratienummer voor personen (Mathematical aspects of the Dutch administration number for persons), Informatie, maandblad voor informatieverwerking, Volume 12, nr. 4, April 1970, pp.162-169.

Verhoeff, J., and W. Goffman, J. Belzer, Inefficiency of the use of boolean functions for information retrieval systems, Communications of the ACM, 4, (1961) 557-558, 594.

Verhoeff, J., Recent invetigations about the radical of a ring, Rapport ZW 1953-007, Math. Centrum Amsterdam, 1953.

Verhoeff, J., On pseudo-convergent sequences, Nederl. Akad. Wetensch. Proc. Ser. A., (Indagationes Math.) 15 (1953) 401-404.

- Introduction
- Using Barcodes
- Zip Codes
- The Universal Product Code
- ISBN Numbers
- The Ultimate System
- References

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