Consider the binary linear code which adds three parity bits C3, C4, C5 to two information...

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Consider the binary linear code which adds three parity bits C3, C4, C5 to two information bits un, u₂ as follows: C3 = U₁, C4 = U₁+U₂, C5 = U₂. a) (1 marks) List all its codewords. b) (2 marks) Does the code (i.e., the set of all codewords) form a subspace of B5? Briefly explain your answer. (Note that binary addition is the same as logical XOR while binary multiplication is the same as logical AND.) c) (1 mark) Determine its minimum distance and state its error correction capability. d) (2 marks) Determine its generator matrix and parity check matrix. e) (1 mark) Suppose the vector (1, 1, 0, 1, 1) is received. Compute the syndrome. (2 marks) Use the syndrome to identify the error bit, if any. Explain your reasoning. f) Consider the binary linear code which adds three parity bits C3, C4, C5 to two information bits un, u₂ as follows: C3 = U₁, C4 = U₁+U₂, C5 = U₂. a) (1 marks) List all its codewords. b) (2 marks) Does the code (i.e., the set of all codewords) form a subspace of B5? Briefly explain your answer. (Note that binary addition is the same as logical XOR while binary multiplication is the same as logical AND.) c) (1 mark) Determine its minimum distance and state its error correction capability. d) (2 marks) Determine its generator matrix and parity check matrix. e) (1 mark) Suppose the vector (1, 1, 0, 1, 1) is received. Compute the syndrome. (2 marks) Use the syndrome to identify the error bit, if any. Explain your reasoning. f)

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This question pertains to a binary linear code used in error detection and correction in data transmission Lets go through each part step by step a List all its codewords Since the code is binary and ... View the full answer