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1. Find the idempotent generator of the binary cyclic code of length 15 with generator polynomial (x² + x + 1)(x+1). 2. (a) Find the generator [polynomial of the binary cyclic code of length 15 with idem- potent generator r3+r6 + x7 + x9 ++11 + x12 + x13 +x14. (b) Find a lower bound on the minimum distance of the code from part (a). 3. Find the dimension of the binary QR code of length 17 with idempotent generator 15 + x16.

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