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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