Linear codes
[57,10,36] over GF(7)
A [57,10] linear code over GF(7) with minimum distance 36, one more than the 35 listed at codetables.de, where the upper bound is 41. Quantavane found it on 25 October 2026.
Checked; it goes to codetables.de with our next batch of results.
The record
| Ours | d = 36 |
|---|---|
| Previous best | d = 35 (upper bound 41) |
| 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 | Two independent programs computed the minimum distance exactly. |
Any two of its 282,475,249 codewords differ in at least 36 of the 57 positions, so it corrects up to 17 errors.
How it was found and checked
A quasi-cyclic code with 3 circulant blocks of size 19, found by a local search over quasi-twisted codes that scores candidates by their lightest sparse codewords and computes the exact distance only for promising ones. Two independent programs computed the minimum distance exactly.
A linear code adds redundancy to data so that errors can be corrected. An [n,k] code over the field GF(q) turns k symbols into n. Its minimum distance d is the fewest positions in which two codewords differ, and the code corrects up to (d−1)/2 errors. Markus Grassl's tables at codetables.de keep the largest d anyone has reached for each n and k. These codes go one higher.
Questions
What is the best known [57,10] code over GF(7)?
Ours, with minimum distance 36; codetables.de listed 35 (read 26 October 2026).
How was it found?
As a quasi-cyclic code with 3 circulant blocks of size 19, by a local search that checks promising candidates exactly.
Is it on codetables.de yet?
Checked; it goes to codetables.de with our next batch of results.