Practic Mode : Paper-II & III On Topic : Computer Networks

Que : 1 . If a code is t-error correcting, the minimum Hamming distance is equal to: (J-2008, J-2009) In order that a code is ′t′ error correcting, the minimum Hamming distance should be: (J-2009)

1. 2t+1
2. 2t
3. 2t-1
4. t-1
Please Select Ans Options .
Explanation

Option 1 is Correct Answer.
The error-detecting and error-correcting properties of a block code depend on its hamming distance.
To reliably DETECT ′t′ errors, you need a distance t+1 code.
To CORRECT t errors, you need a distance 2t+1 code.
If C is linear code over Fq of length n, dimension k, and minimum distance d, we say that C is a q-ary linear [n,k,d] code. As will be seen in our next result, the minimum distance of a code is what determines its error correction ability.
C and correct t errors if and only if dc>= 2t+1.