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I guess the question does not apply just to CS as I'm trying to understand how it applies to RAIDs, but I guess it's maybe the most suitable place to ask anyway.

There's a lot of info that RS codes are often used to implement second parity for RAID-6. There are some systems that implement triple-parity.

Am I right that by using enough Reed-Solomon parity bits I can implement 4-way parity etc., up to arbitrary-way parity (as long the the stripe is long enough, e.g. by writing each n bit stripe as k data bits + t parity bits)?

I'm just surprised why, if it's true, parity counts > 3 are not implemented in any production systems.

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    $\begingroup$ R-S error detection and correction get more complex with increasing length. $\endgroup$
    – user16034
    Nov 14, 2022 at 10:43
  • $\begingroup$ @YvesDaoust do you mean that what I asked is possible, but would just quickly become impractical (prohibitively slow)? $\endgroup$
    – ledonter
    Nov 14, 2022 at 11:00
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    $\begingroup$ It is obviously possible. And probably economically unreasonable. $\endgroup$
    – user16034
    Nov 14, 2022 at 11:01

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A Reed-Solomon code applied to 512-byte (4096-bit) sectors can support up to $n=2^{4096}$ drives in an array, of which any fraction may be parity drives. The limits of real-world RAID setups come from practical considerations, not theory.

RAID can defend against the random failure of up to $t$ drives, but it can't defend against a power surge or fire or software bug or anything else that destroys the entire array. There is some $t_\text{max}$ such that for $t\ge t_\text{max}$ the probability of failure is largely independent of $t$ because failure modes that can't be prevented by RAID dominate. Probably $t_\text{max}\approx 3$.

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More broadly, the issue of repairing Reed-Solomon codes currently employed in industry has been discussed in the literature. It is important to find algorithms with low-bandwidth repair schemes for codes of short lengths with typical redundancies.

A recent paper is a good place to start since it has tables of current best repair schemes for $[n,k]$ Reed-Solomon codes over $\mathbb{GF}(2^8)$ with $4≤n≤16$ and redundancy $r=n−k∈{2,3,4}. $The tables cover most known codes currently used in the distributed storage industry. For convenience, I have reproduced a figure from that paper which has examples of the codes used in industry.

enter image description here

See the paper available here.

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