FA-72243 / Error-correcting codes / Member archive

RS erasure recovery flips the Lagrange denominator · case 03

Recovered symbols are wrong whenever k - 1 is odd.

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 [[[4, 14], [5, 158], [7, 75], [8, 90]], 4]	`[42, 222, 158, 243]`	`[215, 35, 99, 14]`	Failed

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