Information on Result #1304503
Linear OA(3126, 826, F3, 29) (dual of [826, 700, 30]-code), using 80 step Varšamov–Edel lengthening with (ri) = (4, 1, 1, 1, 0, 0, 1, 0, 0, 1, 4 times 0, 1, 6 times 0, 1, 9 times 0, 1, 12 times 0, 1, 15 times 0, 1, 19 times 0) based on linear OA(3112, 732, F3, 29) (dual of [732, 620, 30]-code), using
- construction X applied to Ce(28) ⊂ Ce(27) [i] based on
- linear OA(3112, 729, F3, 29) (dual of [729, 617, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 728 = 36−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(3109, 729, F3, 28) (dual of [729, 620, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 728 = 36−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(30, 3, F3, 0) (dual of [3, 3, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(30, s, F3, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
Mode: Linear.
Optimality
Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OOA(3126, 826, F3, 2, 29) (dual of [(826, 2), 1526, 30]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3126, 826, F3, 3, 29) (dual of [(826, 3), 2352, 30]-NRT-code) | [i] | ||
| 3 | Linear OOA(3126, 826, F3, 4, 29) (dual of [(826, 4), 3178, 30]-NRT-code) | [i] | ||
| 4 | Linear OOA(3126, 826, F3, 5, 29) (dual of [(826, 5), 4004, 30]-NRT-code) | [i] | ||
| 5 | Digital (97, 126, 826)-net over F3 | [i] | ||