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Binary self dual codes, first order Reed Muller codes

Started by jules February 22, 2007
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!     


 



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