Information on Result #614439
Linear OA(776, 16807, F7, 18) (dual of [16807, 16731, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 16806 = 75−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18
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(785, 16817, F7, 18) (dual of [16817, 16732, 19]-code) | [i] | (u, u+v)-Construction | |
| 2 | Linear OA(786, 16819, F7, 18) (dual of [16819, 16733, 19]-code) | [i] | ||
| 3 | Linear OA(787, 16821, F7, 18) (dual of [16821, 16734, 19]-code) | [i] | ||
| 4 | Linear OA(788, 16824, F7, 18) (dual of [16824, 16736, 19]-code) | [i] | ||
| 5 | Linear OA(789, 16836, F7, 18) (dual of [16836, 16747, 19]-code) | [i] | ||
| 6 | Linear OA(790, 16856, F7, 18) (dual of [16856, 16766, 19]-code) | [i] | ||
| 7 | Linear OA(790, 16822, F7, 18) (dual of [16822, 16732, 19]-code) | [i] | Generalized (u, u+v)-Construction | |
| 8 | Linear OOA(776, 10361, F7, 2, 18) (dual of [(10361, 2), 20646, 19]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 9 | Linear OOA(776, 10361, F7, 3, 18) (dual of [(10361, 3), 31007, 19]-NRT-code) | [i] | ||
| 10 | Digital (58, 76, 10361)-net over F7 | [i] | ||
| 11 | Linear OA(789, 16821, F7, 18) (dual of [16821, 16732, 19]-code) | [i] | (u, u−v, u+v+w)-Construction | |
| 12 | Linear OA(790, 16823, F7, 18) (dual of [16823, 16733, 19]-code) | [i] | ||
| 13 | Linear OA(781, 16812, F7, 19) (dual of [16812, 16731, 20]-code) | [i] | ✔ | Construction X with Extended Narrow-Sense BCH Codes |
| 14 | Linear OA(776, 16812, F7, 18) (dual of [16812, 16736, 19]-code) | [i] | ✔ | |
| 15 | Linear OA(787, 16818, F7, 20) (dual of [16818, 16731, 21]-code) | [i] | ✔ | |
| 16 | Linear OA(777, 16818, F7, 18) (dual of [16818, 16741, 19]-code) | [i] | ✔ | |
| 17 | Linear OA(795, 16826, F7, 22) (dual of [16826, 16731, 23]-code) | [i] | ✔ | |
| 18 | Linear OA(779, 16825, F7, 18) (dual of [16825, 16746, 19]-code) | [i] | ✔ | |
| 19 | Linear OA(7102, 16833, F7, 23) (dual of [16833, 16731, 24]-code) | [i] | ✔ | |
| 20 | Linear OA(782, 16833, F7, 18) (dual of [16833, 16751, 19]-code) | [i] | ✔ | |
| 21 | Linear OA(7108, 16839, F7, 24) (dual of [16839, 16731, 25]-code) | [i] | ✔ | |
| 22 | Linear OA(783, 16839, F7, 18) (dual of [16839, 16756, 19]-code) | [i] | ✔ | |
| 23 | Linear OA(787, 16848, F7, 18) (dual of [16848, 16761, 19]-code) | [i] | ✔ | |
| 24 | Linear OA(788, 16854, F7, 18) (dual of [16854, 16766, 19]-code) | [i] | ✔ | |
| 25 | Linear OA(789, 16856, F7, 18) (dual of [16856, 16767, 19]-code) | [i] | ✔ | |
| 26 | Linear OA(7101, 16828, F7, 23) (dual of [16828, 16727, 24]-code) | [i] | ✔ | Construction XX with a Chain of Extended Narrow-Sense BCH Codes |
| 27 | Linear OA(796, 16828, F7, 22) (dual of [16828, 16732, 23]-code) | [i] | ✔ | |
| 28 | Linear OA(788, 16820, F7, 20) (dual of [16820, 16732, 21]-code) | [i] | ✔ | |
| 29 | Linear OA(778, 16820, F7, 18) (dual of [16820, 16742, 19]-code) | [i] | ✔ | |
| 30 | Linear OA(781, 16828, F7, 18) (dual of [16828, 16747, 19]-code) | [i] | ✔ | |