Question

With syndrome decoding, the total no. of possible syndromes is equal to total no. of possible code words. The no. of bits in the code word is 6. The no. of bits which can be corrected by the Linear Binary Code (LBC), which satisfy the Hamming Bound is

• A. 2
• B. 3
• C. 1
• D. 4

Answer 1

The correct option is C 1

$Totalno.ofsyndromes=2^{n-k}$

$Totalno.ofcodewords=2^k$

$\Rightarrow 2^{n-k}=2^k\Rightarrow 2k=n$

LBC is (6, 3)

$UsingHammingBound;2^{n-k}\ge {\sum }_{i=0}^t{}^n{C}_i$

$2^3{\ge }^6{C}_0{+}^6{C}_1$

$8\ge 1+6$

$\therefore t=1$