Information on Result #718918
Linear OA(922, 734, F9, 8) (dual of [734, 712, 9]-code), using construction XX applied to C1 = C([727,5]), C2 = C([0,6]), C3 = C1 + C2 = C([0,5]), and C∩ = C1 ∩ C2 = C([727,6]) based on
- linear OA(919, 728, F9, 7) (dual of [728, 709, 8]-code), using the primitive BCH-code C(I) with length 728 = 93−1, defining interval I = {−1,0,…,5}, and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(919, 728, F9, 7) (dual of [728, 709, 8]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 93−1, defining interval I = [0,6], and designed minimum distance d ≥ |I|+1 = 8 [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 = {−1,0,…,6}, and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(916, 728, F9, 6) (dual of [728, 712, 7]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 93−1, defining interval I = [0,5], and designed minimum distance d ≥ |I|+1 = 7 [i]
- 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
- linear OA(90, 3, F9, 0) (dual of [3, 3, 1]-code) (see above)
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(927, 754, F9, 8) (dual of [754, 727, 9]-code) | [i] | (u, u+v)-Construction | |
| 2 | Linear OOA(922, 734, F9, 2, 8) (dual of [(734, 2), 1446, 9]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(922, 734, F9, 3, 8) (dual of [(734, 3), 2180, 9]-NRT-code) | [i] | ||
| 4 | Digital (14, 22, 734)-net over F9 | [i] | ||
| 5 | Linear OA(923, 751, F9, 8) (dual of [751, 728, 9]-code) | [i] | Varšamov–Edel Lengthening | |
| 6 | Linear OA(924, 846, F9, 8) (dual of [846, 822, 9]-code) | [i] | ||
| 7 | Linear OA(925, 1094, F9, 8) (dual of [1094, 1069, 9]-code) | [i] | ||
| 8 | Linear OA(926, 1485, F9, 8) (dual of [1485, 1459, 9]-code) | [i] | ||
| 9 | Linear OOA(922, 367, F9, 2, 8) (dual of [(367, 2), 712, 9]-NRT-code) | [i] | OOA Folding | |