UGC NET CSE | October 2020 | Part 2 | Question: 31

Question

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. $1111111111$

Answer 1

If the code word arrived is 0000000111 then   it will try to match with the closest valid code

which is 0000011111 with 2 bit error

this proves if min hamming distance is d (here it i 5)  then it can correct max upto (d-1)/2 bit error

for rest valid codewords no of bits in error are more

Hence Option A is right ans