I'm new to this forum and I hope you'll be able to help me.
I have a few exercises about error detection/correction, can you please help me to solve them:

1. The polynomial f(x)=x^6+3x^5+x^4+x^3+2x^2+2x+1 generates a cyclic code of length 15 on F_4. Find a systematic matrix of that code.

2. Find the generator polynomial and the minimal distances of the cyclic codes of length 6.

3. Let C be a linear code on F_3 whose generator matrix is
1 1 1 0
2 0 1 1
Decode the words 1212, 2102, 1111.