Gate2017 ss Q36

0. Consider a binary code that consists of only four valid code words as given below:
00000,01011,10101,11110
Let the minimum Hamming distance of the code be p and the maximum number of erroneous bits that can be corrected by the code be q.
Then the values of p and q are

  • Option : A
  • Explanation :
    Given:
    code1 00000
    code2 01011
    code3 10101
    code4 11110
    Hamming distance between code 1 and code 2 is 3
    Hamming distance between code 1 and code 3 is 3
    Hamming distance between code 1 and code 4 is 4
    Hamming distance between code 2 and code 3 is 4
    Hamming distance between code 2 and code 4 is 3
    Hamming distance between code 3 and code 4 is 3
    So, as per Hamming code, minimum Hamming distance of all code words is considered as Hamming distance i.e., 3 (p).
    Now, the max number of erroneous bits that can be corrected by the Hamming code is 2d + 1
    So,
    So option A is correct.
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