Re: Is this enough for us to have triple-parity RAID?

[Alex <creamyfish@xxxxxxxxx>]

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 <hpa@xxxxxxxxx> wrote:
> Being a generator is a requirement for that.
>
> Alex <creamyfish@xxxxxxxxx> wrote:
>
>>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 <hpa@xxxxxxxxx> wrote:
>>> On 04/17/2012 01:18 PM, David Brown wrote:
>>>>
>>>> For quad parity, we can try g3 = 8 as the obvious next choice in the
>>>> pattern.  Unfortunately, we start hitting conflicts.  To recover
>>missing
>>>> data, we have to solve multiple simultaneous equations over G(2⁸),
>>whose
>>>> coefficients depend on the index numbers of the missing disks.  With
>>>> parity generators (1, 2, 4, 8), some of these combinations of
>>missing
>>>> disk indexes lead to insoluble equations when you have more that 21
>>disks.
>>>>
>>>
>>> That is because 255 = 3*5*17... this means {02}^3 = {08} is not a
>>generator.
>>>
>>>        -hpa
>>>
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