I understand we need a generator to facilitate a 255 data disks array, but 255
sounds like a theoretic limit to me. ZFS now only supports an array of only 9
disks(6 of them are data disks), so having, say, a quad-parity array
of 48 disks(theoretically)
doesn't sound that bad, does it?

Cheers,
Alex

On Fri, Apr 20, 2012 at 11:00 AM, H. Peter Anvin [off-list ref] wrote:

Being a generator is a requirement for that.

Alex [off-list ref] wrote:

quoted

I think when David says 'generator', he doesn't mean the generator of
the order
8 Galois field, he means an arbitrary set  of number in it which can
render the
system of equations solvable to up to a certain number of data
disks(not necessarily
255). He uses a brute-force method with the help of a Python program to
actually
figure that out. It looks pretty cool to me since I have known the
system of 4 equations
generally fails to render a solution for a while, but now I know
exactly how many ways
it may fail...

Cheers,
Alex


On Fri, Apr 20, 2012 at 2:16 AM, H. Peter Anvin [off-list ref] wrote:

quoted

On 04/17/2012 01:18 PM, David Brown wrote:

quoted

For quad parity, we can try g3 = 8 as the obvious next choice in the
pattern.  Unfortunately, we start hitting conflicts.  To recover

missing

quoted

quoted

data, we have to solve multiple simultaneous equations over G(2⁸),

whose

quoted

quoted

coefficients depend on the index numbers of the missing disks.  With
parity generators (1, 2, 4, 8), some of these combinations of

missing

quoted

quoted

disk indexes lead to insoluble equations when you have more that 21

disks.

quoted

quoted

That is because 255 = 3*5*17... this means {02}^3 = {08} is not a

generator.

quoted

       -hpa

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