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Barcodes: References

Feature Column Archive

7. References

Backhouse, J., Retail article numbering and bar codes, Bull. Inst. for Math. and Its Appl., 19 (1983) 17-18.

Beckley, D., An optimum system with modulus, Computer Bulletin (1967) 213-215.

Bressoud, D. and S. Wagon, A Course in Computational Number Theory, Key College Publishing, Emeryville, 2001.

Brown, D., Construction of error detection and error correction codes to any base, Electronic Letters ( (1973) 290.

Briggs, T., Weights for modulus 97 systems, Computer Bulletin, 15 (1971) 79.

Connor, S., The invisible border guard, New Scientist, Jan. 5, 1984, p. 9-14.

Collins, D., and N. Whipple, Using Bar Code, Data Capture Institute, Duxbury, 1990.

Davidson, L., Retrieval of misspelled names in an airline passenger record system, Communications of the ACM, 5 (1962) 169-171.

Ecker, A., and G. Poch, Check character systems, Computing 37 (1986) 277-301.

Gallian, J., The ZIP code bar code, UMAP Journal, 7 (1986) 191-195.

Gallian, J., Assigning driver's license numbers, Mathematics Magazine, 64 (1992) 13-22.

Gallian, J., Check digit methods, International Journal of Applied Engineering Education, 5 (1989) 503-505.

Gallian, J., The mathematics of identification numbers, College Mathematics Journal, 22 (1991) 194-202.

Gallian, J., Error detection methods, ACM Computing Surveys, 28 (1996) 504-517.

Gallian, J., Contempary Abstract Algebra, (5th ed.), Houghton-Mifflin, 2002.

Gallian, J. and S. Winters, Modular arithmetic in the marketplace, American Mathematical Monthly, 95 (1988) 548-551.

Gumm, H., A new class of check digit methods for arbitrary number systems, IEEE Transactions on Information Theory, 31 (1985) 102-105.

Gumm, H., Encoding of numbers to detect typing errors, International Journal of Applied Engineering Education, 2 (1986) 61-65.

Kirtland, J., Identification Numbers and Check Digit Schemes, Mathematical Association of America, Washington, 2001.

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

Winters, S., Error detecting schemes using dihedral groups, UMAP Journal, 11 (1990) 299-308.


  1. Introduction
  2. Barcodes
  3. Zip codes
  4. The Universal Product Code
  5. ISBN Numbers
  6. The Ultimate System
  7. References