# Generator polynomial for reed solomon codes

Started by April 22, 2004
```Can anyone tell me which generator polynomial to use for rs(255,223) code

and also how to find out generator polynomila for other rs codes...(n,k)
sudeep
```
```sudeepkumarts@hotmail.com (Sudeep) wrote in message news:<8dbc777c.0404212307.1b701aac@posting.google.com>...
> Can anyone tell me which generator polynomial to use for rs(255,223) code
>
> and also how to find out generator polynomila for other rs codes...(n,k)
>                  sudeep

Use rspoly(n,k) [or rsgenpoly(n,k) in new Matlab versions] to get the
generator polynomial for any RS(n,k) code. You can also specify the
Primitive Polynomial if you like to.

Rider
```
```sudeepkumarts@hotmail.com (Sudeep) wrote in message news:<8dbc777c.0404212307.1b701aac@posting.google.com>...
> Can anyone tell me which generator polynomial to use for rs(255,223) code
>
> and also how to find out generator polynomila for other rs codes...(n,k)
>                  sudeep
Hi, a Reed-Solomon Code is a code where the generator polynomail
consists of h = n - k , i.e. h = (255-223) = 32, consecutive roots of
a primitive element of the GF(2^m) field.  Thus, for a (255,223) RS
code you would use GF(2^8).  The Galois Field polynomial in GF(2^8)
with primitive element z will be a RS generator: g(x) = (1 - z^1)(1 -
z^2)..(1 - z^32).

Actually, the more general form would be g(x) = (1 - z^{i+1})(1 -
z^{i+2})..(1-z^{i+32}).

An RS code is also a cyclic code, implicating that g(x) should divide
x^n - 1, or in the case above, x^255 - 1.

Hope this helps a bit
Jaco Versfeld
```