Linear codes
[90,11,59] over GF(7)
A [90,11] linear code over GF(7) with minimum distance 59, one more than the 58 listed at codetables.de, where the upper bound is 68. Quantavane found it on 24 October 2026.
Checked; it goes to codetables.de with our next batch of results.
The record
| Ours | d = 59 |
|---|---|
| Previous best | d = 58 (upper bound 68) |
| Previous source | the lower bound listed at codetables.de |
| Found | 24 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 1,977,326,743 codewords differ in at least 59 of the 90 positions, so it corrects up to 29 errors.
How it was found and checked
A quasi-cyclic code with 5 circulant blocks of size 18, 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 [90,11] code over GF(7)?
Ours, with minimum distance 59; codetables.de listed 58 (read 26 October 2026).
How was it found?
As a quasi-cyclic code with 5 circulant blocks of size 18, 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.