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(a) Find the generator matrix for this code

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1 DISCRETE MATHEMATICS 1

Test 2 SPECIMEN 1. (5 pts) Use generating functions to find an if :

an = an−1+ 3n, for n ≥ 1 and a0 = 1.

2. (4 pts) Find the number of ways to select 8 balls from the set of 5 identical red balls, 3 identical yellow balls and 7 identical green balls.

3. (5 pts) Consider the Hamming code defined by the following parity check matrix:

H =

1 0 1 0 1 0 1 0 0 0 1 1 1 1 1 1 0 0 1 1 0

.

(a) Find the generator matrix for this code.

(b) At most one error has arisen during the transmission. What was sent if the received word is (0101010)?

4. (4 pts) Use the extended version of the Euclid’s algorithm to compute EXT-EUCLID(24,42)

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