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Removes reference of Vandermonde matrix.

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The McWilliams-Sloane, "The Theory of Error Correcting Codes" explicitely states that a Vandermonde matrix can have singular submatrix in a finite field.
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Andrea Mazzoleni 2013-09-15 18:50:01 +02:00
parent 91ad1e7f24
commit 397ac3ea8c
1 changed files with 7 additions and 10 deletions
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17
raid.c
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@ -831,19 +831,18 @@ void raid_gen(unsigned level, unsigned char** buffer, unsigned diskmax, unsigned
* the system is not solvable.
*
* Using the primitive polynomial 285, Quad Parity works for up to 21 disks
* with parity generators "1,2,4,8". Changing polynomial to 391, it works for
* up to 27 disks with the same parity generators.
* with parity generators "1,2,4,8". Changing polynomial to 391/451/463/487,
* it works for up to 27 disks with the same parity generators.
* Using different parity generators like "1,7,53,139" it's possible to
* make it working for up to 33 disks. But no more.
*
* A general method working for Quad Parity and more, is to use a
* Vondermonde matrix [3] and [4] or a Cauchy matrix [5], but resulting
* with a slower computational performance, because the coefficients of
* A general method working for Quad Parity and more, is to use a a Cauchy matrix [3],
* but with a slower computational performance, because the coefficients of
* the equations are arbitrarely chosen, and not derived from parity generators.
* This means that you need to use multiplication tables to implement the
* syndrome computation, instead of the fast approach described in [1].
* Note anyway, that there is also a way to implement multiplication tables
* in a very fast way with SSE instructions [6].
* in a very fast way with SSE instructions [4].
*
* In details, Triple Parity is implemented for n disks Di, computing
* the syndromes P,Q,R with:
@ -896,10 +895,8 @@ void raid_gen(unsigned level, unsigned char** buffer, unsigned diskmax, unsigned
* References:
* [1] Anvin, "The mathematics of RAID-6", 2004
* [2] Brown, "Multiple-parity RAID", 2011
* [3] Plank, "A Tutorial on Reed-Solomon Coding for Fault-Tolerance in RAID-like Systems", 1999
* [4] Plank, Ying Ding, "Note: Correction to the 1997 Tutorial on Reed-Solomon Coding", 2003
* [5] Blömer, "An XOR-Based Erasure-Resilient Coding Scheme", 1995
* [6] Plank, "Screaming Fast Galois Field Arithmetic Using Intel SIMD Instructions", 2013
* [3] Blömer, "An XOR-Based Erasure-Resilient Coding Scheme", 1995
* [4] Plank, "Screaming Fast Galois Field Arithmetic Using Intel SIMD Instructions", 2013
*/
/**