Linear codes
[153,10,99] over GF(4)
A [153,10] linear code over GF(4) with minimum distance 99, one more than the 98 listed at codetables.de, where the upper bound is 107. Quantavane found it on 26 October 2026.
Checked; it goes to codetables.de with our next batch of results.
The record
| Ours | d = 99 |
|---|---|
| Previous best | d = 98 (upper bound 107) |
| Previous source | the lower bound listed at codetables.de |
| Found | 26 October 2026 |
| Status | Checked; it goes to codetables.de with our next batch of results. |
| Check | Two independent programs computed the minimum distance; one of them enumerates every codeword. |
Any two of its 1,048,576 codewords differ in at least 99 of the 153 positions, so it corrects up to 49 errors.
How it was found and checked
A quasi-cyclic code with 3 circulant blocks of size 51, 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 [153,10] code over GF(4)?
Ours, with minimum distance 99; codetables.de listed 98 (read 26 October 2026).
How was it found?
As a quasi-cyclic code with 3 circulant blocks of size 51, 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.