Re: Triple parity and beyond

["H. Peter Anvin" <hpa@zytor.com>]

On 11/18/2013 02:35 PM, Andrea Mazzoleni wrote:
> Hi Peter,
> 
> The Cauchy matrix has the mathematical property to always have itself
> and all submatrices not singular. So, we are sure that we can always
> solve the equations to recover the data disks.
> 
> Besides the mathematical proof, I've also inverted all the
> 377,342,351,231 possible submatrices for up to 6 parities and 251 data
> disks, and got an experimental confirmation of this.
> 

Nice.

>
> The only limit is coming from the GF(2^8). You have a maximum number
> of disk = 2^8 + 1 - number_of_parities. For example, with 6 parities,
> you can have no more of 251 data disks. Over this limit it's not
> possible to build a Cauchy matrix.
> 

251?  Not 255?

> Note that instead with a Vandermonde matrix you don't have the
> guarantee to always have all the submatrices not singular. This is the
> reason because using power coefficients, before or late, it happens to
> have unsolvable equations.
> 
> You can find the code that generate the Cauchy matrix with some
> explanation in the comments at (see the set_cauchy() function) :
> 
> http://sourceforge.net/p/snapraid/code/ci/master/tree/mktables.c

OK, need to read up on the theoretical aspects of this, but it sounds
promising.

	-hpa