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Check Digit Schemes

Check Digit Schemes. Jerzy Wojdyło Southeast Missouri State University May 13, 2002. Common Error Patterns. POSTNET. Bar coded digits, 3 short, 2 long, weights 7 4 2 1 0 www.usps.com www.framed.usps.com/cpim/ftp/pubs/pub32.pdf Check equation (for n = 5, 9, 11) . POSTNET. POSTNET.

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Check Digit Schemes

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  1. Check Digit Schemes Jerzy Wojdyło Southeast Missouri State University May 13, 2002

  2. Common Error Patterns

  3. POSTNET • Bar coded digits, 3 short, 2 long, weights 74210 • www.usps.com • www.framed.usps.com/cpim/ftp/pubs/pub32.pdf • Check equation (for n = 5, 9, 11)

  4. POSTNET

  5. POSTNET

  6. POSTNET Advantages • Detects all single errors, • Corrects single error (if corrupted digit is known) • Works for arbitrary length • Disadvantages • Transposition errors are undetected

  7. UPC • Bars and 12 digits UPC = [d1d2d3d4d5d6d7d8d9d10d11d12] w = [3 1 3 1 3 1 3 1 3 1 3 1 ] • Check equation • www.uc-council.com/checkdig.htm • www.upcdatabase.com

  8. UPC

  9. UPC • Advantages • Detects all single errors • Corrects single error (if corrupted digit is known) • Works for arbitrary length • Disadvantages (does not detect) • Jump transpositions • Adjacent transpositions ab ba if |a - b| = 5

  10. EAN • Bars and 13 digits EAN=[d1d2d3d4d5d6d7d8d9d10d11d12d13] w =[ 1 3 1 3 1 3 1 3 1 3 1 3 1 ] • Check equation • Advantages/disadvantages same as UPC • www.ean-int.org

  11. EAN

  12. Credit Cards

  13. Credit Cards • Check digit algorithm(s) • MOD 10 • Luhn Formula • IBM Check • Permutation Check • All do the same • Hans Peter Luhn (1896-1964) • Worked for IBM since 1941 • Example (Excel)

  14. Credit Cards

  15. Credit Cards id , i = 1 i(d) = (0)(124875)(36)(9), i = 2

  16. Credit Cards • Advantages • Detects all single errors • Corrects single error (if corrupted digit is known) • Works for arbitrary length • Disadvantages (does not detect) • Jump transpositions • Adjacent transpositions 09  90 and 90  09

  17. Credit Cards

  18. ISBN • www.ISBN.org • Ten “digits” and three dashes (-) d1d2d3d4d5d6d7d8d9d10 d1,…, d9 = {0, 1, …, 9}; d10 ={0, …, 9, X=10} • Check equation

  19. ISBN 407=11·37

  20. ISBN • Advantages • Detects all single errors • Corrects single error (if corrupted digit is known) • Detects all transposition errors (!!) • Disadvantages • Works for bounded length (≤ 10) • Additional symbol X

  21. Other • US Postal Money Orders • MOD 9 arithmetic • Airline Tickets • MOD 7 arithmetic • Electronic Funds Transfer • MOD 10, weights [3 7 1 3 7 1 3 7 1] • Verhoeff’s Check Digit Scheme • German DM • Dihedral Group D5 multiplication

  22. The End If you blinked and missed it, go to www2.semo.edu/jwojdylo/research.htm

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