Check Digit Schemes

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Check Digit Schemes

• Jerzy Wojdylo
• Southeast Missouri State University
• May 13, 2002

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Common Error Patterns
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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)

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POSTNET
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POSTNET
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POSTNET

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

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UPC

• Bars and 12 digits
• UPC d1 d2 d3 d4 d5 d6 d7 d8 d9 d10 d11 d12
  w 3 1 3 1 3 1 3 1 3 1 3 1
• Check equation
• www.uc-council.com/checkdig.htm
• www.upcdatabase.com

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UPC
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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

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EAN

• Bars and 13 digits
• EANd1 d2 d3 d4 d5 d6 d7 d8 d9 d10 d11 d12 d13
  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

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EAN
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Credit Cards
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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)

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(No Transcript)
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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

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ISBN

• www.ISBN.org
• Ten digits and three dashes (-)
• d1 d2 d3 d4 d5 d6 d7 d8 d9 d10
• d1,, d9 0, 1, , 9 d10 0, , 9, X10
• Check equation

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ISBN
4071137
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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

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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
• Verhoeffs Check Digit Scheme
• German DM
• Dihedral Group D5 multiplication

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The End

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