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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

Check Digit Schemes

Jerzy Wojdyło

Southeast Missouri State University

May 13, 2002

postnet
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)
postnet3
POSTNET

Advantages

    • Detects all single errors,
    • Corrects single error (if corrupted digit is known)
    • Works for arbitrary length
  • Disadvantages
    • Transposition errors are undetected
slide7
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
slide9
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
slide10
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
credit cards1
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)
credit cards3
Credit Cards

id , i = 1

i(d) = (0)(124875)(36)(9), i = 2

credit cards4
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
slide19
ISBN
  • www.ISBN.org
  • Ten “digits” and three dashes (-)

d1d2d3d4d5d6d7d8d9d10

d1,…, d9 = {0, 1, …, 9}; d10 ={0, …, 9, X=10}

  • Check equation
slide20
ISBN

407=11·37

slide21
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
other
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
the end

The End

If you blinked and missed it, go to

www2.semo.edu/jwojdylo/research.htm

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