Information on Result #720115
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]) 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: 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 OA(984, 747, F9, 31) (dual of [747, 663, 32]-code) | [i] | Varšamov–Edel Lengthening | |
| 2 | Linear OA(985, 781, F9, 31) (dual of [781, 696, 32]-code) | [i] | ||
| 3 | Linear OOA(983, 369, F9, 2, 31) (dual of [(369, 2), 655, 32]-NRT-code) | [i] | OOA Folding | |
| 4 | Linear OOA(983, 246, F9, 3, 31) (dual of [(246, 3), 655, 32]-NRT-code) | [i] | ||