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# Check Digit Schemes - PowerPoint PPT Presentation

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

Jerzy Wojdyło

Southeast Missouri State University

May 13, 2002

• 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)

• Detects all single errors,

• Corrects single error (if corrupted digit is known)

• Works for arbitrary length

• Transposition errors are undetected

• 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

• Detects all single errors

• Corrects single error (if corrupted digit is known)

• Works for arbitrary length

• Jump transpositions

• Adjacent transpositions ab ba if |a - b| = 5

• Bars and 13 digits

EAN=[d1d2d3d4d5d6d7d8d9d10d11d12d13] w =[ 1 3 1 3 1 3 1 3 1 3 1 3 1 ]

• Check equation

• www.ean-int.org

• 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)

• Detects all single errors

• Corrects single error (if corrupted digit is known)

• Works for arbitrary length

• Jump transpositions

• Adjacent transpositions 09  90 and 90  09

• www.ISBN.org

• Ten “digits” and three dashes (-)

d1d2d3d4d5d6d7d8d9d10

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

• Check equation

407=11·37

• Detects all single errors

• Corrects single error (if corrupted digit is known)

• Detects all transposition errors (!!)

• Works for bounded length (≤ 10)

• 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

If you blinked and missed it, go to

www2.semo.edu/jwojdylo/research.htm