# Re: Finding generator polynomial over GF(2^3)

From: David Wagner (daw_at_taverner.cs.berkeley.edu)
Date: 10/24/05

Date: Mon, 24 Oct 2005 05:58:48 +0000 (UTC)

>I need to find the generator polynomial of the (9,7) Hamming code over
>GF(2^3). I don't know how to do this.

I don't know how to do this, either. This sounds like a problem
in coding theory, not in cryptography, and my coding theory is
extremely rusty.

If the question is how to express GF(2^3) as a quotient ring of
GF(2)-polynomials, then that one is easier: one finds any polynomial
p(X) that is irreducible over GF(2)[X]; one forms the ideal (p(X)) of
all polynomials in GF(2)[X] that are multiples of p(X); then one forms
GF(2^3) as the quotient ring GF(2)[X]/(p(X)).

But I don't remember how generator polynomials work with Hamming codes,
I'm afraid. Perhaps someone else will know. If not, is there a newsgroup
that is focused on coding theory?

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