Number Theory I need help with Problem 1 part 2. I already have part 1.

the pictures are the problem and part 1

The Hamming code we fix p=2,n=7, and let the number N of messages be 8 . Denote by Fpn the vector space with elements ((ength(a1,,an), where each aiFp. - We say a code is linear if the list of code words forms a linear subspace of Fpn. Let VH be the lisr of code words in the above table. - Show that VH is a linear code. - Give a basis of VH, and give a matrix GH whose image is VH. (1) Let VH List of lode words n me below Table c1=00000000c2=010011001c3=0101011cu=1100110c5=0010111c6=10111010c7=0111100 (3) c5c6=0010.111 (4) To prove VH is a linear code C6C7=C4 c2=10011011110001 (2) c3c4c2c3c4=0101011=10011011100110=c2 C7(1)c8=c2 S9 Total 7+6+5+4+2+1=25 an re .1 Hence VH is a linear code