Consider the linear block code with the codeword defined by

$U=m_1+m_2+m_4+m_5,m_1+m_3+m_4+m_5,m_1+m_2+m_3+m_5,$

$m_1+m_2+m_3+m_4,m_1,m_2,m_3,m_4,m_5$

a$.$ Show the generator matrix.

b$.$ Show the parity$-$check matrix.

c$.$ Find $n,k,$ and $d_{\text{m}\text{i}\text{n}}.$