Information on Result #1313242
Linear OA(985, 781, F9, 31) (dual of [781, 696, 32]-code), using 41 step Varšamov–Edel lengthening with (ri) = (1, 7 times 0, 1, 32 times 0) based on linear OA(983, 738, F9, 31) (dual of [738, 655, 32]-code), using
- construction XX applied to C1 = C([726,27]), C2 = C([0,28]), C3 = C1 + C2 = C([0,27]), and C∩ = C1 ∩ C2 = C([726,28]) [i] based on
- linear OA(979, 728, F9, 30) (dual of [728, 649, 31]-code), using the primitive BCH-code C(I) with length 728 = 93−1, defining interval I = {−2,−1,…,27}, and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(976, 728, F9, 29) (dual of [728, 652, 30]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 93−1, defining interval I = [0,28], and designed minimum distance d ≥ |I|+1 = 30 [i]
- linear OA(982, 728, F9, 31) (dual of [728, 646, 32]-code), using the primitive BCH-code C(I) with length 728 = 93−1, defining interval I = {−2,−1,…,28}, and designed minimum distance d ≥ |I|+1 = 32 [i]
- linear OA(973, 728, F9, 28) (dual of [728, 655, 29]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 93−1, defining interval I = [0,27], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(91, 7, F9, 1) (dual of [7, 6, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(91, 9, F9, 1) (dual of [9, 8, 2]-code), using
- Reed–Solomon code RS(8,9) [i]
- discarding factors / shortening the dual code based on linear OA(91, 9, F9, 1) (dual of [9, 8, 2]-code), using
- linear OA(90, 3, F9, 0) (dual of [3, 3, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(90, s, F9, 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(985, 781, F9, 2, 31) (dual of [(781, 2), 1477, 32]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(985, 781, F9, 3, 31) (dual of [(781, 3), 2258, 32]-NRT-code) | [i] | ||
| 3 | Digital (54, 85, 781)-net over F9 | [i] | ||
| 4 | Linear OOA(985, 390, F9, 2, 31) (dual of [(390, 2), 695, 32]-NRT-code) | [i] | OOA Folding | |