Consider a linear block coding ($($LBC)$)$ scheme with the following generator matrix

[$[$C1$1$ C2$2$Cg]=[$]=[$d1$1$ d2$2$ d$$ d4]$4]$ x G

where the generator matrix is

[111000011$[111000011$

10011001$10011001$

G=$=$

01010101$01010101$

11010010$11010010$

And parity check matrix

H=$=$

[10101010]0110011000011110$[10101010]0110011000011110$

11111111$11111111$

a)$)$ Is this a systematic coding scheme? Why?

b)$)$ Find the equations to find c,$,$ and cg from the information bits [$[$d,$,$ d2$2$ d3$3$ dal c)$)$ Write the error check equations

d)$)$ Find Gx HT

e)$)$ Determine whether the following received codewords are valid ($($error−$-$free)$)$ or not. C1=[10110101]$1=[10110101]$

C2=[10110100]$2=[10110100]$

What is the coding rate of this coding scheme?

What is the minimum distance of this code?

What is the minimum Hamming weights of the rows$$of$$this$$matrix?$?$