Check Digit Schemes

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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

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)
POSTNET

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

id , i = 1

i(d) = (0)(124875)(36)(9), i = 2

Credit Cards
• 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
ISBN
• www.ISBN.org
• Ten “digits” and three dashes (-)

d1d2d3d4d5d6d7d8d9d10

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

• Check equation
ISBN

407=11·37

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

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