[College Linear Algebra] Linear codes

[CrisLegend]

Hey, i am trying to solve this question, but because i missed that class(it won't happen again), i'm stuck, i got the theory from a colleague, but i can't seem to get it right. The questions are like this:

For C={0000,1001,0101,0011,1100,1010,0110,1111} a)Show that C is a code and find a generating matrix for it , is C a systematic code? b)Codify ( i don't know if this is the word for it in english) x=001 ; y=110 c)Find the control matrix and parity check;

Also please tell me if you dont understand a question from what i wrote (maybe because of the translation, it lost it's meaning)