Information on Result #718964
Linear OA(925, 734, F9, 9) (dual of [734, 709, 10]-code), using construction XX applied to C1 = C([727,6]), C2 = C([0,7]), C3 = C1 + C2 = C([0,6]), and C∩ = C1 ∩ C2 = C([727,7]) based on
- 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(922, 728, F9, 8) (dual of [728, 706, 9]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 93−1, defining interval I = [0,7], and designed minimum distance d ≥ |I|+1 = 9 [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 = {−1,0,…,7}, and designed minimum distance d ≥ |I|+1 = 10 [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(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 OOA(925, 734, F9, 2, 9) (dual of [(734, 2), 1443, 10]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(925, 734, F9, 3, 9) (dual of [(734, 3), 2177, 10]-NRT-code) | [i] | ||
| 3 | Digital (16, 25, 734)-net over F9 | [i] | ||
| 4 | Linear OA(926, 749, F9, 9) (dual of [749, 723, 10]-code) | [i] | Varšamov–Edel Lengthening | |
| 5 | Linear OA(927, 831, F9, 9) (dual of [831, 804, 10]-code) | [i] | ||
| 6 | Linear OA(928, 1041, F9, 9) (dual of [1041, 1013, 10]-code) | [i] | ||
| 7 | Linear OA(929, 1360, F9, 9) (dual of [1360, 1331, 10]-code) | [i] | ||
| 8 | Linear OA(930, 1787, F9, 9) (dual of [1787, 1757, 10]-code) | [i] | ||
| 9 | Linear OOA(925, 367, F9, 2, 9) (dual of [(367, 2), 709, 10]-NRT-code) | [i] | OOA Folding | |
| 10 | Linear OOA(925, 244, F9, 3, 9) (dual of [(244, 3), 707, 10]-NRT-code) | [i] | ||