# Am I right that Reed-Solomon codes can be used to implement arbitrary-parity RAID schemes?

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.

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

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 $$t_\text{max}\approx 3$$.
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.