You are Here: Home >< Maths

# Finding cyclic code and generator matrix watch

1. How can I find the cyclic codes of length 6 and dimension 3
I've been told I need to find the irreducible factorisation of x^6 - 1 in F_2[x]
So I've got (x+1)(x-1)(x^2 + x +1)(x^2 - x + 1)
How do I then form the generator matrix from this?
2. Okay so I've just realised that in F2[x]
(x+1)(x-1)(x^2 + x +1)(x^2 - x + 1)
becomes
(x-1)^2 (x^2 + x + 1)^2
So where would I go from here?
3. (Original post by Bruce Harrisface)
Okay so I've just realised that in F2[x]
(x+1)(x-1)(x^2 + x +1)(x^2 - x + 1)
becomes
(x-1)^2 (x^2 + x + 1)^2
So where would I go from here?
So, to get a code of dimension 3, you need to chose from these factors so that you get a polynomial of degree 6-3 = 3. (i.e. if you had a 7th degree poly then for dimension 3 you'd need to factors to get a poly of degree 7-3 = 4).

So work out that poly in the form

Your generator matrix will then have the form

Disclaimer: I should perhaps say that I didn't really know anything about this topic, I've just googled the terms. But I think this is relatively straightforward.

### Related university courses

TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is supported by:
Updated: January 26, 2017
Today on TSR

### Edexcel GCSE Maths Unofficial Markscheme

Find out how you've done here

Poll
Useful resources

### Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

### How to use LaTex

Writing equations the easy way

### Study habits of A* students

Top tips from students who have already aced their exams