FA-72059 / Error-correcting codes / Member archive

Product code corrects the first of several failing intersections · case 04

Two-bit errors are "corrected" into a third wrong bit.

Member previewVariant 4 · 3 implementations · 8 checks per implementation

Case contract

Two-dimensional parity product code. m is a (rows+1) x (cols+1) bit matrix: the last column holds row parities, the last row column parities, and the corner the overall parity, so every full row and column is even. A single failing row and single failing column locate one error (in data or parity) which is flipped. Return [status, data block without parity row/column] with status clean/corrected, or ["uncorrectable", None].

Why this case matters

Simple line-card and tape formats use row/column parity to correct single-bit errors.

One recorded failure

Sample boundary fixture

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

Boundary fixture	Actual	Expected	Outcome
regression [[[0, 0, 1, 0], [1, 0, 1, 1], [0, 1, 0, 1]]]	`["corrected", [[1, 0, 1], [1, 0, 1]]]`	`["uncorrectable", null]`	Failed

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