A linear block code is constructed by taking $k$ information bits and generating a codeword of

length $2k+1$ as follows: the first $k$ bits consist of the information bits, next $k$ bits repeat

the information bits and the last bit is the xor of the first $k$ bits.

a$)$ Is this a systematic code? $($Justify your answer$)$

b$)$ What is the number of valid codewords?

c$)$ Construct the G matrix of this code.

d$)$ Find the $d_{\text{m}\text{i}\text{n}}$ of this code.