FA-71860 / Error-correcting codes / Member archive

Shortened Hamming wraps an out-of-range syndrome · case 05

Double errors in a shortened code are silently "corrected" at a wrong bit.

Member previewVariant 5 · 3 implementations · 8 checks per implementation

Case contract

Single-error-correcting Hamming decoder for a full or shortened code of length n >= 3 (bits 0/1, else None). Positions are 1-based; parity bits sit at powers of two. The syndrome is the XOR of the positions holding a 1. A syndrome above n points outside the shortened code and is "uncorrectable" (data None); otherwise the bit at the syndrome position is flipped. Return [status, data bits from non-power-of-two positions, syndrome].

Why this case matters

Memory and link controllers use (shortened) Hamming codes to repair single-bit upsets.

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, 0, 1, 0, 0, 1, 1, 1, 0]]	`["corrected", [1, 0, 1, 0, 1, 1, 1, 0], 14]`	`["uncorrectable", null, 14]`	Failed

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