Information on Result #614324
Linear OA(746, 16807, F7, 11) (dual of [16807, 16761, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 16806 = 75−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11
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(751, 16815, F7, 11) (dual of [16815, 16764, 12]-code) | [i] | (u, u+v)-Construction | |
| 2 | Linear OA(752, 16818, F7, 11) (dual of [16818, 16766, 12]-code) | [i] | ||
| 3 | Linear OA(753, 16850, F7, 11) (dual of [16850, 16797, 12]-code) | [i] | ||
| 4 | Linear OA(754, 16816, F7, 11) (dual of [16816, 16762, 12]-code) | [i] | Generalized (u, u+v)-Construction | |
| 5 | Linear OOA(746, 11612, F7, 2, 11) (dual of [(11612, 2), 23178, 12]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 6 | Linear OOA(746, 11612, F7, 3, 11) (dual of [(11612, 3), 34790, 12]-NRT-code) | [i] | ||
| 7 | Digital (35, 46, 11612)-net over F7 | [i] | ||
| 8 | Linear OA(753, 16815, F7, 11) (dual of [16815, 16762, 12]-code) | [i] | (u, u−v, u+v+w)-Construction | |
| 9 | Linear OA(754, 16823, F7, 11) (dual of [16823, 16769, 12]-code) | [i] | ||
| 10 | Linear OA(751, 16812, F7, 12) (dual of [16812, 16761, 13]-code) | [i] | ✔ | Construction X with Extended Narrow-Sense BCH Codes |
| 11 | Linear OA(746, 16812, F7, 11) (dual of [16812, 16766, 12]-code) | [i] | ✔ | |
| 12 | Linear OA(757, 16818, F7, 13) (dual of [16818, 16761, 14]-code) | [i] | ✔ | |
| 13 | Linear OA(747, 16818, F7, 11) (dual of [16818, 16771, 12]-code) | [i] | ✔ | |
| 14 | Linear OA(765, 16826, F7, 15) (dual of [16826, 16761, 16]-code) | [i] | ✔ | |
| 15 | Linear OA(749, 16825, F7, 11) (dual of [16825, 16776, 12]-code) | [i] | ✔ | |
| 16 | Linear OA(772, 16833, F7, 16) (dual of [16833, 16761, 17]-code) | [i] | ✔ | |
| 17 | Linear OA(752, 16833, F7, 11) (dual of [16833, 16781, 12]-code) | [i] | ✔ | |
| 18 | Linear OA(778, 16839, F7, 17) (dual of [16839, 16761, 18]-code) | [i] | ✔ | |
| 19 | Linear OA(787, 16848, F7, 18) (dual of [16848, 16761, 19]-code) | [i] | ✔ | |
| 20 | Linear OA(793, 16854, F7, 19) (dual of [16854, 16761, 20]-code) | [i] | ✔ | |
| 21 | Linear OA(799, 16856, F7, 20) (dual of [16856, 16757, 21]-code) | [i] | ✔ | |
| 22 | Linear OA(7102, 16863, F7, 20) (dual of [16863, 16761, 21]-code) | [i] | ✔ | |
| 23 | Linear OA(7100, 16859, F7, 20) (dual of [16859, 16759, 21]-code) | [i] | ✔ | |
| 24 | Linear OA(7101, 16862, F7, 20) (dual of [16862, 16761, 21]-code) | [i] | ✔ | |
| 25 | Linear OA(771, 16828, F7, 16) (dual of [16828, 16757, 17]-code) | [i] | ✔ | Construction XX with a Chain of Extended Narrow-Sense BCH Codes |
| 26 | Linear OA(763, 16820, F7, 14) (dual of [16820, 16757, 15]-code) | [i] | ✔ | |
| 27 | Linear OA(766, 16828, F7, 15) (dual of [16828, 16762, 16]-code) | [i] | ✔ | |
| 28 | Linear OA(758, 16820, F7, 13) (dual of [16820, 16762, 14]-code) | [i] | ✔ | |
| 29 | Linear OA(751, 16828, F7, 11) (dual of [16828, 16777, 12]-code) | [i] | ✔ | |
| 30 | Linear OA(747, 16819, F7, 11) (dual of [16819, 16772, 12]-code) | [i] | ✔ | Construction X4 with Extended Narrow-Sense BCH Codes |
| 31 | Linear OA(762, 16824, F7, 13) (dual of [16824, 16762, 14]-code) | [i] | ✔ | |