Information on Result #719992
Linear OA(981, 739, F9, 30) (dual of [739, 658, 31]-code), using construction XX applied to C1 = C([63,91]), C2 = C([66,92]), C3 = C1 + C2 = C([66,91]), and C∩ = C1 ∩ C2 = C([63,92]) based on
- linear OA(976, 728, F9, 29) (dual of [728, 652, 30]-code), using the primitive BCH-code C(I) with length 728 = 93−1, defining interval I = {63,64,…,91}, and designed minimum distance d ≥ |I|+1 = 30 [i]
- linear OA(973, 728, F9, 27) (dual of [728, 655, 28]-code), using the primitive BCH-code C(I) with length 728 = 93−1, defining interval I = {66,67,…,92}, and designed minimum distance d ≥ |I|+1 = 28 [i]
- 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 = {63,64,…,92}, and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(970, 728, F9, 26) (dual of [728, 658, 27]-code), using the primitive BCH-code C(I) with length 728 = 93−1, defining interval I = {66,67,…,91}, and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(92, 8, F9, 2) (dual of [8, 6, 3]-code or 8-arc in PG(1,9)), using
- discarding factors / shortening the dual code based on linear OA(92, 9, F9, 2) (dual of [9, 7, 3]-code or 9-arc in PG(1,9)), using
- Reed–Solomon code RS(7,9) [i]
- discarding factors / shortening the dual code based on linear OA(92, 9, F9, 2) (dual of [9, 7, 3]-code or 9-arc in PG(1,9)), 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 OOA(981, 737, F9, 2, 30) (dual of [(737, 2), 1393, 31]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(981, 737, F9, 3, 30) (dual of [(737, 3), 2130, 31]-NRT-code) | [i] | ||
| 3 | Digital (51, 81, 737)-net over F9 | [i] | ||
| 4 | Linear OOA(981, 369, F9, 2, 30) (dual of [(369, 2), 657, 31]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(981, 246, F9, 3, 30) (dual of [(246, 3), 657, 31]-NRT-code) | [i] | ||