Decoders

Lookup table lookup-table standard

Exhaustively maps each syndrome to a correction for one fixed, small code and noise model; exact lookup becomes impractical as the syndrome space grows.

Type: exact-small · Noise setting: one known erasure location with perfect parity information

For this code: Recovery consumes the externally supplied location as well as the two parity outcomes. Grassl, Beth, and Pellizzari prove the one-erasure capability; removing the location changes the error set and invalidates this recovery table.

References: grassl1997erasure, gingrich2003optical

Lookup table lookup-table standard

Exhaustively maps each syndrome to a correction for one fixed, small code and noise model; exact lookup becomes impractical as the syndrome space grows.

Type: exact-small · Noise setting: one unknown-position Pauli fault with perfect stabilizer readout

For this code: Here the table is an accept-or-reject detector: zero syndrome accepts and any nonzero syndrome rejects. It is not a correction decoder because equal-type faults at different positions collide, and a guessed repair can differ from the actual fault by a weight-two logical operator.

References: gottesman2016small, linke2017faulttolerant