GATE | Gate IT 2007 | Question 43

An error correcting code has the following code words: 
00000000, 00001111, 01010101, 10101010, 11110000.
What is the maximum number of bit errors that can be corrected ?

(A)

0

(B)

1

(C)

2

(D)

3

Answer: (B)

Explanation:

While transmitting the data through the channel, noise may be added to the data and thus, may cause errors in the data. Hamming code errors CANNOT be DETECTED if one code converts into another. 

detection possible up to ( hamming distance – 1) = 4 – 1 = 3 bits

correction possible up to { [ ( hamming distance – 1) / 2 ]}

                                     = \left \lfloor\frac{Hamming \ Distance-1}{2} \right \rfloor

                                     =

                                     =  

                                     = 1 bit

Therefore, option B is the correct answer. 

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