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Let C be the binary cyclic code of length 15 generated by g(x) = x 5 + x 4 + x 2 + 1. (a)

Let C be the binary cyclic code of length 15 generated by g(x) = x5 + x4 + x2 + 1. (a) Show that g(x) is a valid generator polynomial. (b) Compute the parity check polynomial for C. (c) Determine the dimension of C and the number of codewords in C.

(d) Construct generator and parity check matrices for the code.

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