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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


  • Check digit schemes
    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



    Check digit schemes
    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


    Check digit schemes
    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 cards2
    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


    Check digit schemes
    ISBN

    • www.ISBN.org

    • Ten “digits” and three dashes (-)

      d1d2d3d4d5d6d7d8d9d10

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

    • Check equation


    Check digit schemes
    ISBN

    407=11·37


    Check digit schemes
    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