Problem $1$

Consider a parity$-$check code defined by its parity$-$check matrix $H$ given below

It defines a code, used for transmission over a BSC with crossover probability $p.$ Codeword

$x$ is transmitted and we denote the sequence at the output of the channel by $y.$

$1)$minimum distance of code given a parity check matrix

$2)$generator matrix

$3)$all code words