FA-71883 / Error-correcting codes / Member archive

SECDED flips the bit before the syndrome position · case 03

Single-bit errors are moved rather than corrected.

Member previewVariant 3 · 3 implementations · 8 checks per implementation

Case contract

Extended Hamming (8,4) SECDED decoder. r[0] is the overall parity bit; r[1..7] are Hamming positions 1..7 with data at 3, 5, 6, 7. s is the XOR of set positions 1..7 and p the parity of all eight bits. s=0,p=0: "clean"; p=1: single error at position s (s=0 means the overall parity bit) - "corrected"; s!=0,p=0: ["double", None]. Return [status, data]. Non-binary or wrong-length input returns None.

Why this case matters

ECC DRAM controllers must distinguish correctable single-bit errors from uncorrectable double-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 [[1, 0, 0, 1, 1, 0, 0, 0]]	`["corrected", [1, 0, 1, 0]]`	`["corrected", [1, 0, 0, 1]]`	Failed

MEMBER ARCHIVE

The complete case is available to members.

This record includes three runnable implementations, regression fixtures, execution results, and source hashes.

Member access is invitation-based. Sign in with your invited account to inspect the sources.