Quantum codes
[[70,42,9]]_5
A [[70,42]] quantum code over qudits (q = 5) with minimum distance 9, one more than the 8 listed at codetables.de, where the upper bound is 14. Quantavane found it on 25 October 2026.
Checked; it goes to codetables.de with our next batch of results.
The record
| Ours | d = 9 |
|---|---|
| Previous best | d = 8 (upper bound 14) |
| Previous source | the lower bound listed at codetables.de |
| Found | 25 October 2026 |
| Status | Checked; it goes to codetables.de with our next batch of results. |
| Check | The distance was computed by the search and again by a separate program. |
It encodes 42 qudits into 70 and corrects up to 4 arbitrary errors.
How it was found and checked
A random Hermitian self-orthogonal code over GF(25). The distance was computed by the search and again by a separate program.
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 [[70,42]] quantum code over qudits (q = 5)?
Ours, with minimum distance 9; codetables.de listed 8 (read 26 October 2026).
How was it built?
A random Hermitian self-orthogonal code over GF(25).
Is it on codetables.de yet?
Checked; it goes to codetables.de with our next batch of results.