5. Linear codes The code words U1 001010, u2111101, 43 001001, u4 = 101111. form a basis for a (6,4) linear binary code. i. Write down a generator matrix for this code. ii. Construct code words for the messages 1110, 1001 and 0110. iii. Write down the parity check matrix for this code. iv. Find syndromes for the received words 101010, 100101 and 001110.

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