The answer to exercise marked [BB]can be found in the Back of the Book.
Consider the following alternative check for correctness of an ISBN number. Instead of (6), the check digit a10 is determined by the rule a1 + a2 +… a9 + a10 = 0 (mod 11).
(a) [BB] Express this rule in the form w · a = 0 (mod 11) for some vectors w and a.
(b) Show that this rule detects an error in a single digit.
(c) Show that this rule does not detect a transposition of two (different) digits.
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