# Coding Theory - Constructing Binary (n, M, d) - Codes

• Dec 30th 2013, 03:34 PM
joeDIT
Coding Theory - Constructing Binary (n, M, d) - Codes
Is there a method for constructing Binary (n, M, d) - codes. For e.g. the code (7, 2, 7) is just the Rep code (0000000, 1111111). But this was just by looking at it.What is the method for e.g.'s such as (8, 4, 5) or (7, 3, 5)? Don't want an answer just don't want to have to do trial and error approach because time is tight in exams. There must be a method to check. Any help greatly appreciated.
PS
n - lengths of codewords
M - number of codewords
d - minimum distance
• Dec 30th 2013, 04:54 PM
romsek
Re: Coding Theory - Constructing Binary (n, M, d) - Codes
Not really sure what you are asking but here.
• Dec 31st 2013, 12:04 AM
joeDIT
Re: Coding Theory - Constructing Binary (n, M, d) - Codes
My question was, what is (if there is) the method that one would use to construct a binary code when given different parameters? Preferably without using method of bounds (Griesmer Bound). Any help is greatly appreciated.
• Dec 31st 2013, 12:16 AM
romsek
Re: Coding Theory - Constructing Binary (n, M, d) - Codes
Quote:

Originally Posted by joeDIT
My question was, what is (if there is) the method that one would use to construct a binary code when given different parameters? Preferably without using method of bounds (Griesmer Bound). Any help is greatly appreciated.

The BCH codes are pretty close to that. You're not going to be able to independently select all 3 parameters. Obviously d is going to depend on n and M. There are tables of BCH codes that have been worked out for a variety of n,M that also have known d. Is that not good enough?
• Dec 31st 2013, 12:24 AM
joeDIT
Re: Coding Theory - Constructing Binary (n, M, d) - Codes
Well there is usually a question that will contain these as a part and you are given the parameters? I won't have a table of BCH codes with me you know? It has to be explained and i assume using a method? One is generally a rep code and the other two; either one will be possible to construct a binary code and one generally wont be.. So its safe to assume that you can't just 'guess' and go rep code, yes,no, you know? Do you know of any other methods?
• Dec 31st 2013, 12:42 AM
romsek
Re: Coding Theory - Constructing Binary (n, M, d) - Codes
Quote:

Originally Posted by joeDIT
Well there is usually a question that will contain these as a part and you are given the parameters? I won't have a table of BCH codes with me you know? It has to be explained and i assume using a method? One is generally a rep code and the other two; either one will be possible to construct a binary code and one generally wont be.. So its safe to assume that you can't just 'guess' and go rep code, yes,no, you know? Do you know of any other methods?

The only thing you're going to be able to generate on the fly like this is some sort of parity code. Maybe take a look at this.
• Dec 31st 2013, 12:43 AM
joeDIT
Re: Coding Theory - Constructing Binary (n, M, d) - Codes
Apparently you do actually just try and make the code and if you cant then it doesn't exist there is no exact method. Thanks anyways romsek.