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Shortening BCH codes?

Started by gct August 4, 2009
Quick question I'm sure someone can put to bed easily:  Is it possible to
shorten BCH codes in the same way that you shorten Reed-Solomon?   My
instinct is yes, but I want to make sure it's not going to do anything evil
like reduce the minimum distance...
On 8/4/2009 10:58 AM, gct wrote:
> Quick question I'm sure someone can put to bed easily: Is it possible to > shorten BCH codes in the same way that you shorten Reed-Solomon? My > instinct is yes, but I want to make sure it's not going to do anything evil > like reduce the minimum distance...
Of course it's possible, and it's commonly done. It won't reduce the minimum distance since shortening just reduces the set of codewords used, it doesn't move or alter them. -- Eric Jacobsen Minister of Algorithms Abineau Communications http://www.abineau.com
Eric Jacobsen  <eric.jacobsen@ieee.org> wrote:

>On 8/4/2009 10:58 AM, gct wrote:
>> Quick question I'm sure someone can put to bed easily: Is it possible to >> shorten BCH codes in the same way that you shorten Reed-Solomon? My >> instinct is yes, but I want to make sure it's not going to do anything evil >> like reduce the minimum distance...
>Of course it's possible, and it's commonly done. It won't reduce the >minimum distance since shortening just reduces the set of codewords >used, it doesn't move or alter them.
Actually, shortening a BCH code can increase (not reduce) the minimum distance. For a trivial example of this, shorten the code to contain a single information bit. But there are less trivial examples. Steve
On 8/4/2009 11:51 AM, Steve Pope wrote:
> Eric Jacobsen<eric.jacobsen@ieee.org> wrote: > >> On 8/4/2009 10:58 AM, gct wrote: > >>> Quick question I'm sure someone can put to bed easily: Is it possible to >>> shorten BCH codes in the same way that you shorten Reed-Solomon? My >>> instinct is yes, but I want to make sure it's not going to do anything evil >>> like reduce the minimum distance... > >> Of course it's possible, and it's commonly done. It won't reduce the >> minimum distance since shortening just reduces the set of codewords >> used, it doesn't move or alter them. > > Actually, shortening a BCH code can increase (not reduce) the > minimum distance. For a trivial example of this, shorten > the code to contain a single information bit. But there > are less trivial examples. > > Steve
Yup. If the minimum distance codewords are removed from the original codeword set in the shortening process then the min. dist. in the remaining set is, naturally, larger. Sometimes it's worth carefully picking the shortening method for this reason. -- Eric Jacobsen Minister of Algorithms Abineau Communications http://www.abineau.com