Question

$\text{A linear block code (LBC) has a minimum distance of}{d}_{\text{min}.}\text{If this LBC has to detect upto 3 bit errors and simultaneously correct upto 2 bit errors, then}{d}_{\text{min}}\text{should satisfy the condition}$

• A. $d_{\text{min}}\le 6$
• B. $d_{\text{min}}\le 5$
• C. $d_{\text{min}}\ge 5$
• D. $d_{\text{min}}\ge 6$

Answer 1

The correct option is D $d_{\text{min}}\ge 6$

$\text{The condition to be satisfied to detect upto}"e_d"\text{bit errors and simultaneously correct upto}"e_c"\text{bit errors is,}$

$d_{\text{min}}\ge e_d+e_c+1$
$\text{so,}{d}_{\text{min}}\ge 3+2+1$
$d_{\text{min}}\ge 6$