# Need help on meaning of these terminology of reed-muller code.

Started by August 18, 2007
```Hi,

I want to know meaning of the word below:
-  "Self dual"   , What's for?
-  "Dual code"   ,What's for?
-  "Soft decision"  ,What's for?
and what's about algebraic code ?
what's about equivalent relation in the coding theory?

Phongphan porana.
phongphanp@yahoo.com

```
```On Aug 18, 2:15 pm, kongp <phongphan...@gmail.com> wrote:
> Hi,
>
>  I want to know meaning of the word below:
>   -  "Self dual"   , What's for?
>   -  "Dual code"   ,What's for?
>   -  "Soft decision"  ,What's for?
>   and what's about algebraic code ?
>         what's about equivalent relation in the coding theory?
>
> Phongphan porana.
> phongph...@yahoo.com

If you just want the definitions:

- A dual code: a code that is in the null/dual space of a
given code, in the appropriate space.  Any codeword
of a code is orthogonal to any codeword from its dual
code.

- A self-dual code is if its dual code is itself.

- Soft-decision:  there's some abuse of definition, but
usually this means the likelihood ratio of the most
likely bits, or sequence of bits that give a codeword.

What for?  Self-dual codes are important because some
of the best codes known are of this type, and one can
study them using the self-dual property.

http://www.research.att.com/~njas/doc/self.ps

These are questions best answered through a coding
theory book.  You don't say what your background is,
so I don't know what exactly to recommend.

Julius

```
```On Aug 19, 3:16 am, julius <juli...@gmail.com> wrote:
> On Aug 18, 2:15 pm, kongp <phongphan...@gmail.com> wrote:
>
> > Hi,
>
> >  I want to know meaning of the word below:
> >   -  "Self dual"   , What's for?
> >   -  "Dual code"   ,What's for?
> >   -  "Soft decision"  ,What's for?
> >   and what's about algebraic code ?
> >         what's about equivalent relation in the coding theory?
>
> > Thamk for your help,
> > Phongphan porana.
> > phongph...@yahoo.com
>
> If you just want the definitions:
>
>  - A dual code: a code that is in the null/dual space of a
>    given code, in the appropriate space.  Any codeword
>    of a code is orthogonal to any codeword from its dual
>    code.
>
>  - A self-dual code is if its dual code is itself.
>
>  - Soft-decision:  there's some abuse of definition, but
>    usually this means the likelihood ratio of the most
>    likely bits, or sequence of bits that give a codeword.
>
> What for?  Self-dual codes are important because some
> of the best codes known are of this type, and one can
> study them using the self-dual property.
>
> http://www.research.att.com/~njas/doc/self.ps
>
> These are questions best answered through a coding
> theory book.  You don't say what your background is,
> so I don't know what exactly to recommend.
>
> Julius

First, Thank for your quickly response.

But, I think that your hints is not practical(more mathematical
theory) for beginner like me
, one like in most books , and there are other approach ? Such as One
may have simple example and simple litle prctical useage for this
themes. and continually, I want to ask about meanning of these word:

- syndome
- erasure
- error-location polynomial

and  programming suit for large node than hardware approach , right?

Best regard,
Phongphan Porana.
phongphanp@yahoo.com

```
```On Aug 18, 3:50 pm, kongp <phongphan...@gmail.com> wrote:

> First, Thank for your quickly response.
>
>  But, I think that your hints is not practical(more mathematical
> theory) for beginner like me
>  , one like in most books , and there are other approach ? Such as One
> may have simple example and simple litle prctical useage for this
> themes. and continually, I want to ask about meanning of these word:
>
> - syndome
> - erasure
> - error-location polynomial
>
> and  programming suit for large node than hardware approach , right?
>
> Best regard,
> Phongphan Porana.
> phongph...@yahoo.com

You don't say at all what your background is, but regardless
what you are asking about is not a trivial area.  So you can
continue to expect a "simple" answer, but I don't know if you
will ever find a "simple" answer.

I am going to assume that you at least know some digital
logic and a little bit of algebra.  In that case, Blahut's book
"Algebraic Codes for Data Transmission" is quite good.
I don't know if there's anything more elementary that doesn't
reduce the knowledge into something not useful, sorry.

Good luck.
Julius

```
```On Aug 19, 6:15 am, julius <juli...@gmail.com> wrote:
> On Aug 18, 3:50 pm, kongp <phongphan...@gmail.com> wrote:
>
>
>
>
>
> > First, Thank for your quickly response.
>
> >  But, I think that your hints is not practical(more mathematical
> > theory) for beginner like me
> >  , one like in most books , and there are other approach ? Such as One
> > may have simple example and simple litle prctical useage for this
> > themes. and continually, I want to ask about meanning of these word:
>
> > - syndome
> > - erasure
> > - error-location polynomial
>
> > and  programming suit for large node than hardware approach , right?
>
> > Best regard,
> > Phongphan Porana.
> > phongph...@yahoo.com
>
> You don't say at all what your background is, but regardless
> what you are asking about is not a trivial area.  So you can
> continue to expect a "simple" answer, but I don't know if you
> will ever find a "simple" answer.
>
> I am going to assume that you at least know some digital
> logic and a little bit of algebra.  In that case, Blahut's book
> "Algebraic Codes for Data Transmission" is quite good.
> I don't know if there's anything more elementary that doesn't
> reduce the knowledge into something not useful, sorry.
>
> Good luck.
> Julius- Hide quoted text -
>
> - Show quoted text -

OK, I'm an electronic engineer that interesting in science and
Technology :
Algebra(linear code)
Topology(for dual code)
Complex Number
Telecommunication( Optic fibre , RF )
Physics
chemical process
Image processing
Signal processing(Sound,acoustics)
etc.

definitions like in mathematics dictionary. the meaning is not clear
in real world, one had to be define on primary mathematical ideas, so
your definite be only approximately of any idea, right . It's useful
when Programming is on, I'm admit in that point. and I'm suspect idea
on what's "orthogonal" ? and why best codes come
from self-dual code ? If it's not wasteful time, The answer may in
another form, physics or technical term.

Thank you very much...
phongphan Porana.
phongphanp@yahoo.com

```