Information on Result #1304542
Linear OA(3128, 789, F3, 30) (dual of [789, 661, 31]-code), using 42 step Varšamov–Edel lengthening with (ri) = (3, 1, 1, 0, 1, 0, 0, 1, 4 times 0, 1, 6 times 0, 1, 9 times 0, 1, 12 times 0) based on linear OA(3118, 737, F3, 30) (dual of [737, 619, 31]-code), using
- construction XX applied to C1 = C([727,27]), C2 = C([0,28]), C3 = C1 + C2 = C([0,27]), and C∩ = C1 ∩ C2 = C([727,28]) [i] based on
- linear OA(3115, 728, F3, 29) (dual of [728, 613, 30]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {−1,0,…,27}, and designed minimum distance d ≥ |I|+1 = 30 [i]
- linear OA(3112, 728, F3, 29) (dual of [728, 616, 30]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 36−1, defining interval I = [0,28], and designed minimum distance d ≥ |I|+1 = 30 [i]
- linear OA(3118, 728, F3, 30) (dual of [728, 610, 31]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {−1,0,…,28}, and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(3109, 728, F3, 28) (dual of [728, 619, 29]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 36−1, defining interval I = [0,27], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(30, 6, F3, 0) (dual of [6, 6, 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
- 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 (see above)
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(3128, 789, F3, 2, 30) (dual of [(789, 2), 1450, 31]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3128, 789, F3, 3, 30) (dual of [(789, 3), 2239, 31]-NRT-code) | [i] | ||
| 3 | Linear OOA(3128, 789, F3, 4, 30) (dual of [(789, 4), 3028, 31]-NRT-code) | [i] | ||
| 4 | Linear OOA(3128, 789, F3, 5, 30) (dual of [(789, 5), 3817, 31]-NRT-code) | [i] | ||
| 5 | Digital (98, 128, 789)-net over F3 | [i] | ||