Linear codes
[102,10,73] over GF(9)
A [102,10] linear code over GF(9) with minimum distance 73, one more than the 72 listed at codetables.de, where the upper bound is 82. Quantavane found it on 24 October 2026.
Sent to Markus Grassl for codetables.de on 24 October 2026; the table shows it once he adds it.
The record
| Ours | d = 73 |
|---|---|
| Previous best | d = 72 (upper bound 82) |
| Previous source | the lower bound listed at codetables.de |
| Found | 24 October 2026 |
| Status | Sent to Markus Grassl for codetables.de on 24 October 2026; the table shows it once he adds it. |
| Check | Two independent programs computed the minimum distance; one of them enumerates every codeword. |
Any two of its 3,486,784,401 codewords differ in at least 73 of the 102 positions, so it corrects up to 36 errors.
How it was found and checked
A quasi-twisted code with 3 blocks of size 34 and twist w, 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; one of them enumerates every codeword.
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 [102,10] code over GF(9)?
Ours, with minimum distance 73; codetables.de listed 72 (read 26 October 2026).
How was it found?
As a quasi-twisted code with 3 blocks of size 34 and twist w, by a local search that checks promising candidates exactly.
Is it on codetables.de yet?
Sent to Markus Grassl for codetables.de on 24 October 2026; the table shows it once he adds it.