On Feb 22, 6:51 am, "jules" <juliec_1...@yahoo.ca> wrote:
> Hello. I've been trying to learn more about special linear codes such as
> Reed-Muller codes, binary self-dual and self-orthogonal codes, and
> stumbled upon a couple of problems.
>
> For example, is there a binary self-dual (10,5,4) code? In some articles
> I've read, it was 'shown' that it does exist, but my colleagues say it
> does not. So I am rather confused as to who to believe. Now just for a
> binary (10,5) self dual code, what is an example of a generator matrix for
> the code? Finally, are first order Reed Muller codes self-orthogonal
> and/or self-dual?
>
> Basically, I'm confused and having trouble of whether certain types of
> codes are self-dual/orthogonal or not.
>
> Some help and clarification would be very much appreciated!
Not sure if this will give a direct answer, but if anybody
knows the existence of self-dual binary codes, it's probably
Neil Sloane:
http://www.research.att.com/~njas/doc/pless.ps
The problem is often it is easier to prove that something
exists (here it is!) rather than it does not exist :-P.
Reed-Muller codes are self-orthogonal, but not all of them
are self-dual. I think only RM((m-1)/2,m) codes are
self-dual, but not 100% sure.
Julius
Reply by jules●February 22, 20072007-02-22
Hello. I've been trying to learn more about special linear codes such as
Reed-Muller codes, binary self-dual and self-orthogonal codes, and
stumbled upon a couple of problems.
For example, is there a binary self-dual (10,5,4) code? In some articles
I've read, it was 'shown' that it does exist, but my colleagues say it
does not. So I am rather confused as to who to believe. Now just for a
binary (10,5) self dual code, what is an example of a generator matrix for
the code? Finally, are first order Reed Muller codes self-orthogonal
and/or self-dual?
Basically, I'm confused and having trouble of whether certain types of
codes are self-dual/orthogonal or not.
Some help and clarification would be very much appreciated!