Quantum codes
[[39,23,5]]
A [[39,23]] qubit code with minimum distance 5, one more than the 4 listed at codetables.de, where the upper bound is 6. Quantavane found it on 24 October 2026.
Sent to Markus Grassl for codetables.de on 25 October 2026; the table shows it once he adds it.
The record
| Ours | d = 5 |
|---|---|
| Previous best | d = 4 (upper bound 6) |
| Previous source | the lower bound listed at codetables.de |
| Found | 24 October 2026 |
| Status | Sent to Markus Grassl for codetables.de on 25 October 2026; the table shows it once he adds it. |
| Check | Two separate programs computed the full weight distribution. |
It encodes 23 qubits into 39 and corrects up to 2 arbitrary errors.
How it was found and checked
A quasi-twisted code over GF(4) through quantum Construction X. Two separate programs computed the full weight distribution.
A quantum error-correcting code protects qubits the way a linear code protects symbols. An [[n,k]] code spreads k qubits over n, and with minimum distance d it corrects up to (d−1)/2 errors. Codes with k = 0, single entangled states of n qubits, are listed too. Markus Grassl's tables at codetables.de keep the largest d known for each n and k, for qubits and for larger dimensions q (qudits).
Questions
What is the best known [[39,23]] qubit code?
Ours, with minimum distance 5; codetables.de listed 4 (read 26 October 2026).
How was it built?
A quasi-twisted code over GF(4) through quantum Construction X.
Is it on codetables.de yet?
Sent to Markus Grassl for codetables.de on 25 October 2026; the table shows it once he adds it.