Information on Result #719021
Linear OA(929, 735, F9, 11) (dual of [735, 706, 12]-code), using construction XX applied to C1 = C([82,91]), C2 = C([84,92]), C3 = C1 + C2 = C([84,91]), and C∩ = C1 ∩ C2 = C([82,92]) based on
- linear OA(925, 728, F9, 10) (dual of [728, 703, 11]-code), using the primitive BCH-code C(I) with length 728 = 93−1, defining interval I = {82,83,…,91}, and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(925, 728, F9, 9) (dual of [728, 703, 10]-code), using the primitive BCH-code C(I) with length 728 = 93−1, defining interval I = {84,85,…,92}, and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(928, 728, F9, 11) (dual of [728, 700, 12]-code), using the primitive BCH-code C(I) with length 728 = 93−1, defining interval I = {82,83,…,92}, and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(922, 728, F9, 8) (dual of [728, 706, 9]-code), using the primitive BCH-code C(I) with length 728 = 93−1, defining interval I = {84,85,…,91}, and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(91, 4, F9, 1) (dual of [4, 3, 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 OOA(929, 478, F9, 2, 11) (dual of [(478, 2), 927, 12]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(929, 478, F9, 3, 11) (dual of [(478, 3), 1405, 12]-NRT-code) | [i] | ||
| 3 | Digital (18, 29, 478)-net over F9 | [i] | ||
| 4 | Linear OOA(929, 367, F9, 2, 11) (dual of [(367, 2), 705, 12]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(929, 245, F9, 3, 11) (dual of [(245, 3), 706, 12]-NRT-code) | [i] | ||