FPGA Central

Howdilliy Doodily Neighbourinos...

can anyone tell me the resgister length and feed-back connections for
generation of an M-sequence of length 63...

Mucho Appreciado
DD

"porterboy" <[email protected]> wrote in message
news:[email protected] om...
> Howdilliy Doodily Neighbourinos...
>
> can anyone tell me the resgister length and feed-back connections
for
> generation of an M-sequence of length 63...
>
> Mucho Appreciado
> DD

Look on the Xilinx site.

Regards
Ian

let's see.... 63=2^6-1, so you want m=6. then you need a minimal
polynomial, which you can get from any book on coding theory in the
library.

good luck,
julius

On Wed, 17 Dec 2003, porterboy wrote:

> Howdilliy Doodily Neighbourinos...
>
> can anyone tell me the resgister length and feed-back connections for
> generation of an M-sequence of length 63...
>
> Mucho Appreciado
> DD
>

--
The most rigorous proofs will be shown by vigorous handwaving.
http://www.mit.edu/~kusuma

opinion of author is not necessarily of the institute

Julius Kusuma <[email protected]> wrote in message

> let's see.... 63=2^6-1, so you want m=6. then you need a minimal
> polynomial, which you can get from any book on coding theory in the
> library.

You mean I should actually do some work?
I thought comp.dsp was here so lazy Engineers like me
wouldnt have to work :-P

Well, I found my answer, page 32 of the following presentation...
http://calliope.uwaterloo.ca/~ggong/lecture1-Bochum.pdf

By the way, Ian, could you give me a specific page on the Xilinx
website... if I search for m-sequences it throws up about 500 pages...

Cheerio
DD

Julius Kusuma <[email protected]> wrote
> let's see.... 63=2^6-1, so you want m=6. then you need a minimal
> polynomial, which you can get from any book on coding theory in the
> library.

I remember that polynomials which generate maximal length sequences
are "primitive irreducible polynomials" (according to Blahut's
definition in "Theory and Practice of Error Control Codes"). I also
thought this is more than just a minimal polynomial (of a primitive
element in GF{64} - finite field with 64 elements). I could be wrong.
Julius - Could you please throw some light on this?

thanks and warm regards,
Kiran

On Thu, 18 Dec 2003, Kiran.T wrote:

> I remember that polynomials which generate maximal length sequences
> are "primitive irreducible polynomials" (according to Blahut's
> definition in "Theory and Practice of Error Control Codes"). I also
> thought this is more than just a minimal polynomial (of a primitive
> element in GF{64} - finite field with 64 elements). I could be wrong.
> Julius - Could you please throw some light on this?
>
> thanks and warm regards,
> Kiran

kiran, you are correct that all you need is a primitive irreducible
polynomial. however, since all galois fields of the same order are really
the same thing, i prefer to use the minimal polynomial. just a personal
preference.

if you use minimal polynomials to represent finite fields, it is unique to
that order, and it is a divisor of (x^p)^n-x.

regards,
julius

--
The most rigorous proofs will be shown by vigorous handwaving.
http://www.mit.edu/~kusuma

opinion of author is not necessarily of the institute

Julius Kusuma <[email protected]> wrote in message news:<Pine.GSO.4.55L.0312170940590.20850@departmen t-of-alchemy.mit.edu>...
> let's see.... 63=2^6-1, so you want m=6. then you need a minimal
> polynomial, which you can get from any book on coding theory in the
> library.
>
> good luck,
> julius
>
> On Wed, 17 Dec 2003, porterboy wrote:
>
> > Howdilliy Doodily Neighbourinos...
> >
> > can anyone tell me the resgister length and feed-back connections for
> > generation of an M-sequence of length 63...
> >
> > Mucho Appreciado
> > DD
> >

Everything can be found at:
http://www.ece.cmu.edu/~koopman/lfsr/

Henk van Kampen
www.mediatronix.com

Kiran.T wrote:

> "primitive irreducible polynomials"

I thought "primitive" and "irreducible" are distinct?
--
% Randy Yates % "...the answer lies within your soul
%% Fuquay-Varina, NC % 'cause no one knows which side
%%% 919-577-9882 % the coin will fall."
%%%% <[email protected]> % 'Big Wheels', *Out of the Blue*, ELO
http://home.earthlink.net/~yatescr

"Randy Yates" <[email protected]> wrote in message
news:MSvEb.617$[email protected] k.net...
> I thought "primitive" and "irreducible" are distinct?

Primitive implies irreducible, but not vice versa, i.e., "primitive
irreducible polynomial" means the same thing as "primitive polynomial".
Every irredicible polynomial has generating elements of maximal order, where
'g' is a generating element mod P if, for every polynomial Q, either Q=0 mod
P, or there is some x such that Q=g^x mod P. The polynomial is primitive if
x is such a generator.

Generating M-sequences with LFSRs requires primitive polynomials, because
each iteration maps x^a -> x^(a+1) mod P. The requirement for primitive
polynomials makes this iteration visit all non-zero values mod P.