<p>I am studying Information theory, coding theory in particular at the moment, and I am having trouble determining how many different cycles are defined by a certain generator polinomial?</p>

<p>Given a polinomial, for example $g(p)=p^6+p^3+1$, and the length of the code $n = 9$ how can I determine the number of different cycles that are defined? Everything is in modulo 2 arithmetics. </p>

<p>I know that the cycles (001)(010)(100) and (011)(110)(101) are defined, but how can I find the rest of them?</p>

<p>I also wonder if there is an explicit formula that can return me the result, maybe based on the different powers in the generating polinomial?</p>

<p>Thank you for helping me.</p>

CC BY-SA 3.0
2015-05-26T06:25:08.873Z
please specify that your code is binary. your cycle notation is nonstandard. are those codewords?
kodlu
CC BY-SA 3.0
2015-06-12T05:48:51.147Z
Cross posted in [Math.SE](http://math.stackexchange.com/q/1298374/11619).
Jyrki Lahtonen
<coding-theory>
Number of different cycles in cyclic codes with length n
Mark
# Number of different cycles in cyclic codes with length n

(Asked by: username_0 on 2015-05-25)

I am studying Information theory, coding theory in particular at the moment, and I am having trouble determining how many different cycles are defined by a certain generator polinomial?

Given a polinomial, for example $g(p)=p^6+p^3+1$, and the length of the code $n = 9$ how can I determine the number of different cycles that are defined? Everything is in modulo 2 arithmetics.

I know that the cycles (001)(010)(100) and (011)(110)(101) are defined, but how can I find the rest of them?

I also wonder if there is an explicit formula that can return me the result, maybe based on the different powers in the generating polinomial?

Thank you for helping me.

**Tags:** coding-theory

> **Comments:**
> **username_1**: please specify that your code is binary. your cycle notation is nonstandard. are those codewords?  
> **username_2**: Cross posted in [Math.SE](http://math.stackexchange.com/q/1298374/11619).  

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## 0 answers

