UGC NET CSE | January 2017 | Part 3 | Question: 64

Question

Let C be a binary linear code with minimum distance $2t+1$ then it can correct upto ___ bits of error

• A. $t+1$
• B. $t$
• C. $t-2$
• D. $t/2$

Answer 1

Option B)

Question should be framed correctly. In a set of codewords with hamming distance 2t + 1 , t errors can be corrected.

Answer 2

A code is t-errors correcting if, and only if, the minimum Hamming distance between any two of its codewords is at least 2t+1. 

Answer 3

Hamming Distance

Detection: Minimum Distance = Number of error bits to be detected + 1

Correction: Minimum Distance = 2 * Number of error bits to be corrected + 1

Here,

Given, Minimum Distance = 2t + 1

According to the correction formula,

Number of error bits to be corrected = (Minimum Distance - 1)/2

Number of error bits to be corrected = (2t + 1 - 1)/2  = 2t / 2 = t (Answer)

Answer 4

B should be the Answer

because in "t" bit Error Detaction we need minimum distance = t+1

and in "t" bit Error Correction we need minimum distance = 2t+1

for good read

http://www.eecs.umich.edu/courses/eecs373.w05/lecture/errorcode.html#:~:text=Minimum%20Hamming%20distance%20for%20error%20correction,of%202d%20%2B%201%20is%20required.