Information on Result #718879
Linear OA(919, 734, F9, 7) (dual of [734, 715, 8]-code), using construction XX applied to C1 = C([727,4]), C2 = C([0,5]), C3 = C1 + C2 = C([0,4]), and C∩ = C1 ∩ C2 = C([727,5]) based on
- linear OA(916, 728, F9, 6) (dual of [728, 712, 7]-code), using the primitive BCH-code C(I) with length 728 = 93−1, defining interval I = {−1,0,…,4}, and designed minimum distance d ≥ |I|+1 = 7 [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(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(913, 728, F9, 5) (dual of [728, 715, 6]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 93−1, defining interval I = [0,4], and designed minimum distance d ≥ |I|+1 = 6 [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(923, 816, F9, 7) (dual of [816, 793, 8]-code) | [i] | (u, u+v)-Construction | |
| 2 | Linear OA(924, 946, F9, 7) (dual of [946, 922, 8]-code) | [i] | ||
| 3 | Linear OOA(919, 734, F9, 2, 7) (dual of [(734, 2), 1449, 8]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 4 | Linear OOA(919, 734, F9, 3, 7) (dual of [(734, 3), 2183, 8]-NRT-code) | [i] | ||
| 5 | Digital (12, 19, 734)-net over F9 | [i] | ||
| 6 | Linear OA(920, 756, F9, 7) (dual of [756, 736, 8]-code) | [i] | Varšamov–Edel Lengthening | |
| 7 | Linear OA(921, 878, F9, 7) (dual of [878, 857, 8]-code) | [i] | ||
| 8 | Linear OA(922, 1194, F9, 7) (dual of [1194, 1172, 8]-code) | [i] | ||
| 9 | Linear OA(923, 1707, F9, 7) (dual of [1707, 1684, 8]-code) | [i] | ||
| 10 | Linear OA(924, 2459, F9, 7) (dual of [2459, 2435, 8]-code) | [i] | ||
| 11 | Linear OOA(919, 367, F9, 2, 7) (dual of [(367, 2), 715, 8]-NRT-code) | [i] | OOA Folding | |