Let C be a linear [n, k]-code with alphabet GF(q). Let C+ be any code obtained from C by lengthening, that is, first adding one extra bit to every codeword of C and then adding one extra row to a generating matrix for C while maintaining linear independence. (a) Find the length and dimension of C+. (b) Suppose C is perfect and 1-error-correcting. Prove C+ cannot be 1-errorcorrecting.

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A: See below steps for complete explanation.

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