So, there was a question on my exam last year as follows:
Using idempotents, determine the number of proper cyclic codes of length 17.
I got the question right, but I can't remember how to do the question. I know I need to
- Find the classes mod 17 and what's in those classes
- Determine the corresponding idempotent polynomials (which don't need to be written explicitly)
- Write the overall idempotent polynomial
- Determine the number of cyclic codes
- Determine the proper number of cyclic codes
So, I'm getting hung up on 1 and 5.
Questions:
- How do I figure out what the "classes" are and what they contain?
- How do I figure out the proper number of cyclic codes?
If someone could point me in the right direction it would be appreciated.