FA-72257 / Error-correcting codes / Member archive

RS erasure recovery evaluates data at zero-based points · case 02

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

Member previewVariant 2 · 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, 191], [5, 97], [3, 23]], 3]	`[173, 191, 141]`	`[191, 141, 23]`	Failed

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