Information on Result #684728
Linear OA(785, 16832, F7, 19) (dual of [16832, 16747, 20]-code), using construction X applied to C([0,9]) ⊂ C([0,7]) based on
- linear OA(781, 16808, F7, 19) (dual of [16808, 16727, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 16808 | 710−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- linear OA(761, 16808, F7, 15) (dual of [16808, 16747, 16]-code), using the expurgated narrow-sense BCH-code C(I) with length 16808 | 710−1, defining interval I = [0,7], and minimum distance d ≥ |{−7,−6,…,7}|+1 = 16 (BCH-bound) [i]
- linear OA(74, 24, F7, 3) (dual of [24, 20, 4]-code or 24-cap in PG(3,7)), 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 OA(786, 16833, F7, 19) (dual of [16833, 16747, 20]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(787, 16834, F7, 19) (dual of [16834, 16747, 20]-code) | [i] | ||
| 3 | Linear OOA(785, 16832, F7, 2, 19) (dual of [(16832, 2), 33579, 20]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 4 | Linear OOA(785, 16832, F7, 3, 19) (dual of [(16832, 3), 50411, 20]-NRT-code) | [i] | ||
| 5 | Digital (66, 85, 16832)-net over F7 | [i] | ||
| 6 | Linear OA(786, 16834, F7, 19) (dual of [16834, 16748, 20]-code) | [i] | Construction X with Varšamov Bound | |
| 7 | Linear OA(787, 16836, F7, 19) (dual of [16836, 16749, 20]-code) | [i] | ||
| 8 | Linear OOA(785, 8416, F7, 2, 19) (dual of [(8416, 2), 16747, 20]-NRT-code) | [i] | OOA Folding | |
| 9 | Linear OOA(785, 5610, F7, 3, 19) (dual of [(5610, 3), 16745, 20]-NRT-code) | [i] | ||
| 10 | Linear OOA(785, 1870, F7, 19, 19) (dual of [(1870, 19), 35445, 20]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |