The ISBN of a book is a unique 13-digit code', also known as ISBN-13, that encodes information about the publisher, registrant, place of publication, and so on. If the ISBN-13 of a book is Y142Y3 · ·· Y13, then it must satisfy the following congruence: yi + 3y2 + y3 + 3y4 + y5 + 3y6 + y7 + 3ys + y9 + 3y10 + y11 + 3y12+ y13 = 0 (mod 10). (a) Find a book at home and take a picture of it showing the 13-digit ISBN. Then show that its ISBN satisfies this congruence. (b) Suppose you have another book whose ISBN is partially erased so that you can't read the fifth digit y5. Can you compute it using the above congruence? Explain why you can always do this. 978 - 1? 215 8 7 6 6 0 (c) What if two digits were removed from an ISBN-13? Would you be able to recover the ISBN? Demon- strate using your book from (a) as an example.
The ISBN of a book is a unique 13-digit code', also known as ISBN-13, that encodes information about the publisher, registrant, place of publication, and so on. If the ISBN-13 of a book is Y142Y3 · ·· Y13, then it must satisfy the following congruence: yi + 3y2 + y3 + 3y4 + y5 + 3y6 + y7 + 3ys + y9 + 3y10 + y11 + 3y12+ y13 = 0 (mod 10). (a) Find a book at home and take a picture of it showing the 13-digit ISBN. Then show that its ISBN satisfies this congruence. (b) Suppose you have another book whose ISBN is partially erased so that you can't read the fifth digit y5. Can you compute it using the above congruence? Explain why you can always do this. 978 - 1? 215 8 7 6 6 0 (c) What if two digits were removed from an ISBN-13? Would you be able to recover the ISBN? Demon- strate using your book from (a) as an example.
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter2: The Integers
Section2.7: Introduction To Coding Theory (optional)
Problem 12E: Suppose that the check digit is computed as described in Example . Prove that transposition errors...
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