FA-72258 / Error-correcting codes / Member archive

RS erasure recovery evaluates data at zero-based points · case 03

Recovered data is shifted by one position and includes a value at x = 0.

Member previewVariant 3 · 3 implementations · 8 checks per implementation

Case contract

Systematic Reed-Solomon erasure code over GF(257): the k data symbols are the values of a degree < k polynomial at x = 1..k, and any symbol is its value at another x. Given surviving shares [x, y] (duplicates allowed if they agree; conflicting duplicates return None; y is reduced mod 257), recover the k data symbols by Lagrange interpolation over the k shares with the smallest x. Fewer than k distinct x values returns None.

Why this case matters

Distributed storage rebuilds lost data fragments from any k surviving fragments.

One recorded failure

Sample boundary fixture

This sample comes from the broken implementation of a controlled reproducer.

Boundary fixture	Actual	Expected	Outcome
regression [[[1, 224], [5, 68], [4, 8]], 3]	`[171, 224, 86]`	`[224, 86, 14]`	Failed

MEMBER ARCHIVE

The complete case is available to members.

This record includes three runnable implementations, regression fixtures, execution results, and source hashes.

Member access is invitation-based. Sign in with your invited account to inspect the sources.