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From: bharat pathak on 9 Aug 2010 22:58
I have one question regarding maximal length lfsr.
if i need to generate 32 bit lfsr then how many
primitive polynomials exist such that the generated
sequence is always maximal length.

Regards
Bharat
From: dvsarwate on 9 Aug 2010 23:10
On Aug 9, 9:58 pm, "bharat pathak" <bharat(a)n_o_s_p_a_m.arithos.com>
wrote:
> I have one question regarding maximal length lfsr.
> if i need to generate 32 bit lfsr then how many
> primitive polynomials exist such that the generated
> sequence is always maximal length.
>
> Regards
> Bharat


There are phi(2^n - 1) binary primitive polynomials
of degree n where phi is called Euler's totient
function (no, that is not a typo, it really is
totient and not quotient). The value of phi(x)
depends on the factorization of x as a product of
prime powers. For more details, see, for example,

http://en.wikipedia.org/wiki/Euler%27s_totient_function

Hope this helps

--Dilip Sarwate
From: dvsarwate on 9 Aug 2010 23:43
On Aug 9, 10:10 pm, dvsarwate <dvsarw...(a)gmail.com> mistakenly wrote:

>
> There are phi(2^n - 1) binary primitive polynomials
> of degree n where phi is called Euler's totient
> function

Actually, the number of primitive polynomials
is phi(2^n - 1)/n.

phi(2^n - 1) is the number of primitive elements
of GF(2^n), and each primitive polynomial has n
of these primitive elements as roots. For example,
GF(2^5) has 30 primitive elements and there are
6 primitive polynomials of degree 5.

The error is regretted.

--Dilip Sarwate

From: Rafael Deliano on 10 Aug 2010 01:54
About 20% of the available will do:
http://www.embeddedFORTH.de/temp/wust.pdf
That includes the reverse polynomials.

MfG JRD
From: Clay on 10 Aug 2010 10:03
On Aug 9, 11:10 pm, dvsarwate <dvsarw...(a)gmail.com> wrote:
> On Aug 9, 9:58 pm, "bharat pathak" <bharat(a)n_o_s_p_a_m.arithos.com>
> wrote:
>
> > I have one question regarding maximal length lfsr.
> > if i need to generate 32 bit lfsr then how many
> > primitive polynomials exist such that the generated
> > sequence is always maximal length.
>
> > Regards
> > Bharat
>
> There are phi(2^n - 1) binary primitive polynomials
> of degree n where phi is called Euler's totient
> function (no, that is not a typo, it really is
> totient and not quotient).  The value of phi(x)
> depends on the factorization of x as a product of
> prime powers.  For more details, see, for example,
>
> http://en.wikipedia.org/wiki/Euler%27s_totient_function
>
> Hope this helps
>
> --Dilip Sarwate

Here is some stuff I wrote about the Totient function. You may find it
interesting.

http://www.claysturner.com/dsp/totient.pdf

Clay

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