Code word - Digital logic

Question 1 UGC NET June-2020
Consider a code with only four valid code words: 0000000000, 0000011111, 1111100000, and 1111111111. This code has distance 5. If the code word arrived is 0000000111 then the original code word must be __.

A – 0000011111

B – 0000000000

C – 1111100000

D – 1111111111

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Answer : A
correcting t-bit error hamming distance should be 2t+1.
So, 2t + 1 = 5
t = 2
It means the hamming distance between the code-word 0000000111 and give option should be of 2-bits.