GATE | GATE-IT-2004 | Question 84

Consider a parity check code with three data bits and four parity check bits. Three of the code words are 0101011, 1001101 and 1110001. Which of the following are also code words?
I. 0010111             II. 0110110         III. 1011010             IV. 0111010

(A) I and III
(B) I, II and III
(C) II and IV
(D) I, II, III and IV


Answer: (A)

Explanation:
a = 0101011
b = 1001101
c = 1110001

XOR of two codewords is itself a codeword.

a XOR c = 1011010
Thus, III is a codeword.

d = 1011010
b XOR d = 0010111
Thus, I is a codeword.


Thus, option (A) is correct.


Please comment below if you find anything wrong in the above post.


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