Information on Result #614303
Linear OA(736, 16807, F7, 9) (dual of [16807, 16771, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 16806 = 75−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9
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(740, 16815, F7, 9) (dual of [16815, 16775, 10]-code) | [i] | (u, u+v)-Construction | |
| 2 | Linear OA(741, 16818, F7, 9) (dual of [16818, 16777, 10]-code) | [i] | ||
| 3 | Linear OA(742, 16849, F7, 9) (dual of [16849, 16807, 10]-code) | [i] | ||
| 4 | Linear OOA(736, 9464, F7, 2, 9) (dual of [(9464, 2), 18892, 10]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 5 | Linear OOA(736, 9464, F7, 3, 9) (dual of [(9464, 3), 28356, 10]-NRT-code) | [i] | ||
| 6 | Digital (27, 36, 9464)-net over F7 | [i] | ||
| 7 | Linear OA(741, 16812, F7, 10) (dual of [16812, 16771, 11]-code) | [i] | ✔ | Construction X with Extended Narrow-Sense BCH Codes |
| 8 | Linear OA(736, 16812, F7, 9) (dual of [16812, 16776, 10]-code) | [i] | ✔ | |
| 9 | Linear OA(747, 16818, F7, 11) (dual of [16818, 16771, 12]-code) | [i] | ✔ | |
| 10 | Linear OA(738, 16815, F7, 9) (dual of [16815, 16777, 10]-code) | [i] | ✔ | |
| 11 | Linear OA(739, 16820, F7, 9) (dual of [16820, 16781, 10]-code) | [i] | ✔ | |
| 12 | Linear OA(754, 16825, F7, 12) (dual of [16825, 16771, 13]-code) | [i] | ✔ | |
| 13 | Linear OA(740, 16826, F7, 9) (dual of [16826, 16786, 10]-code) | [i] | ✔ | |
| 14 | Linear OA(760, 16831, F7, 13) (dual of [16831, 16771, 14]-code) | [i] | ✔ | |
| 15 | Linear OA(768, 16839, F7, 15) (dual of [16839, 16771, 16]-code) | [i] | ✔ | |
| 16 | Linear OA(777, 16848, F7, 16) (dual of [16848, 16771, 17]-code) | [i] | ✔ | |
| 17 | Linear OA(783, 16854, F7, 17) (dual of [16854, 16771, 18]-code) | [i] | ✔ | |
| 18 | Linear OA(789, 16856, F7, 18) (dual of [16856, 16767, 19]-code) | [i] | ✔ | |
| 19 | Linear OA(766, 16833, F7, 14) (dual of [16833, 16767, 15]-code) | [i] | ✔ | Construction XX with a Chain of Extended Narrow-Sense BCH Codes |
| 20 | Linear OA(761, 16833, F7, 13) (dual of [16833, 16772, 14]-code) | [i] | ✔ | |
| 21 | Linear OA(753, 16820, F7, 12) (dual of [16820, 16767, 13]-code) | [i] | ✔ | |
| 22 | Linear OA(741, 16828, F7, 9) (dual of [16828, 16787, 10]-code) | [i] | ✔ | |
| 23 | Linear OA(747, 16819, F7, 11) (dual of [16819, 16772, 12]-code) | [i] | ✔ | Construction X4 with Extended Narrow-Sense BCH Codes |