FA-71865 / Error-correcting codes / Member archive

Hamming encoder parity covers multiples of the parity position · case 05

Codewords fail to decode as clean.

Member previewVariant 5 · 3 implementations · 8 checks per implementation

Case contract

Hamming(7,4) encoder: data d1..d4 go to positions 3, 5, 6, 7; the parity bit at position p (1, 2, 4) is the XOR of all other positions whose index has bit p set. Return the 7-bit codeword (position 1 first).

Why this case matters

Low-cost telemetry links protect nibbles with Hamming(7,4).

One recorded failure

Sample boundary fixture

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

Boundary fixture	Actual	Expected	Outcome
regression [[1, 1, 1, 0]]	`[1, 1, 1, 0, 1, 1, 0]`	`[0, 0, 1, 0, 1, 1, 0]`	Failed

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