Answer to Question #282799 in Discrete Mathematics for V.kathiravan

Question

What and Define The Hamming Metric with example in mathematical foundations of computer science

Answer 1

For the vectors $a=(a_1,a_2,\ldots,a_n)\in\{0,1\}^n$ and $b=(b_1,b_2,\ldots,b_n)\in\{0,1\}^n$ the Hamming Metric $\rho_H$ is defined as

$\rho_H(a,b)=\sum\limits_{i=1}^n|a_i-b_i|.$

For example, for $a=(1,0,1,1)\in\{0,1\}^4$ and $b=(0,0,1,0)\in\{0,1\}^4$ the Hamming Metric $\rho_H(a,b)$ is equal to

$\rho_H(a,b)=|1-0|+|0-0|+|1-1|+|1-0|=1+0+0+1=2.$