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!

# Binary self dual codes, first order Reed Muller codes

Started by ●February 22, 2007

Reply by ●February 22, 20072007-02-22

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