Information on Result #704519
Linear OA(3104, 741, F3, 26) (dual of [741, 637, 27]-code), using construction XX applied to C1 = C([340,364]), C2 = C([342,365]), C3 = C1 + C2 = C([342,364]), and C∩ = C1 ∩ C2 = C([340,365]) based on
- linear OA(397, 728, F3, 25) (dual of [728, 631, 26]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {340,341,…,364}, and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(397, 728, F3, 24) (dual of [728, 631, 25]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {342,343,…,365}, and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(3103, 728, F3, 26) (dual of [728, 625, 27]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {340,341,…,365}, and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(391, 728, F3, 23) (dual of [728, 637, 24]-code), using the primitive BCH-code C(I) with length 728 = 36−1, defining interval I = {342,343,…,364}, and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(31, 7, F3, 1) (dual of [7, 6, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(31, s, F3, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- 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
Mode: Constructive and 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(3104, 526, F3, 2, 26) (dual of [(526, 2), 948, 27]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(3104, 526, F3, 3, 26) (dual of [(526, 3), 1474, 27]-NRT-code) | [i] | ||
| 3 | Linear OOA(3104, 526, F3, 4, 26) (dual of [(526, 4), 2000, 27]-NRT-code) | [i] | ||
| 4 | Linear OOA(3104, 526, F3, 5, 26) (dual of [(526, 5), 2526, 27]-NRT-code) | [i] | ||
| 5 | Digital (78, 104, 526)-net over F3 | [i] | ||
| 6 | Linear OA(3111, 764, F3, 26) (dual of [764, 653, 27]-code) | [i] | Varšamov–Edel Lengthening | |
| 7 | Linear OA(3112, 774, F3, 26) (dual of [774, 662, 27]-code) | [i] | ||
| 8 | Linear OA(3113, 788, F3, 26) (dual of [788, 675, 27]-code) | [i] | ||
| 9 | Linear OA(3114, 806, F3, 26) (dual of [806, 692, 27]-code) | [i] | ||
| 10 | Linear OA(3115, 829, F3, 26) (dual of [829, 714, 27]-code) | [i] | ||
| 11 | Linear OA(3116, 857, F3, 26) (dual of [857, 741, 27]-code) | [i] | ||
| 12 | Linear OA(3117, 889, F3, 26) (dual of [889, 772, 27]-code) | [i] | ||
| 13 | Linear OA(3118, 925, F3, 26) (dual of [925, 807, 27]-code) | [i] | ||
| 14 | Linear OOA(3104, 370, F3, 2, 26) (dual of [(370, 2), 636, 27]-NRT-code) | [i] | OOA Folding | |
| 15 | Linear OOA(3104, 247, F3, 3, 26) (dual of [(247, 3), 637, 27]-NRT-code) | [i] | ||
| 16 | Linear OOA(3104, 185, F3, 4, 26) (dual of [(185, 4), 636, 27]-NRT-code) | [i] | ||