Question: 3.27 Define a linear (5,3) code over GF(4) by the generator matrix 1 -C 0 0 1 0 0 1 1 1 2 3 1

3.27 Define a linear (5,3) code over GF(4) by the generator matrix 1 -C 0 0 1 0 0 1 1 1 2

3.27 Define a linear (5,3) code over GF(4) by the generator matrix 1 -C 0 0 1 0 0 1 1 1 2 3 1 (a) Find the parity-check matrix. (b) Prove that this is a single-error-correcting code. (c) Prove that it is a double-erasure-correcting code. (d) Prove that it is a perfect code. 3.27 Define a linear (5,3) code over GF(4) by the generator matrix 1 -C 0 0 1 0 0 1 1 1 2 3 1 (a) Find the parity-check matrix. (b) Prove that this is a single-error-correcting code. (c) Prove that it is a double-erasure-correcting code. (d) Prove that it is a perfect code

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