Information on Result #614407
Linear OA(766, 16807, F7, 16) (dual of [16807, 16741, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 16806 = 75−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16
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(774, 16816, F7, 16) (dual of [16816, 16742, 17]-code) | [i] | (u, u+v)-Construction | |
| 2 | Linear OA(775, 16818, F7, 16) (dual of [16818, 16743, 17]-code) | [i] | ||
| 3 | Linear OA(776, 16827, F7, 16) (dual of [16827, 16751, 17]-code) | [i] | ||
| 4 | Linear OA(778, 16835, F7, 16) (dual of [16835, 16757, 17]-code) | [i] | ||
| 5 | Linear OOA(766, 8444, F7, 2, 16) (dual of [(8444, 2), 16822, 17]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 6 | Linear OOA(766, 8444, F7, 3, 16) (dual of [(8444, 3), 25266, 17]-NRT-code) | [i] | ||
| 7 | Digital (50, 66, 8444)-net over F7 | [i] | ||
| 8 | Linear OA(777, 16819, F7, 16) (dual of [16819, 16742, 17]-code) | [i] | (u, u−v, u+v+w)-Construction | |
| 9 | Linear OA(778, 16821, F7, 16) (dual of [16821, 16743, 17]-code) | [i] | ||
| 10 | Linear OA(771, 16812, F7, 17) (dual of [16812, 16741, 18]-code) | [i] | ✔ | Construction X with Extended Narrow-Sense BCH Codes |
| 11 | Linear OA(766, 16812, F7, 16) (dual of [16812, 16746, 17]-code) | [i] | ✔ | |
| 12 | Linear OA(777, 16818, F7, 18) (dual of [16818, 16741, 19]-code) | [i] | ✔ | |
| 13 | Linear OA(768, 16815, F7, 16) (dual of [16815, 16747, 17]-code) | [i] | ✔ | |
| 14 | Linear OA(769, 16820, F7, 16) (dual of [16820, 16751, 17]-code) | [i] | ✔ | |
| 15 | Linear OA(784, 16825, F7, 19) (dual of [16825, 16741, 20]-code) | [i] | ✔ | |
| 16 | Linear OA(770, 16826, F7, 16) (dual of [16826, 16756, 17]-code) | [i] | ✔ | |
| 17 | Linear OA(790, 16831, F7, 20) (dual of [16831, 16741, 21]-code) | [i] | ✔ | |
| 18 | Linear OA(772, 16833, F7, 16) (dual of [16833, 16761, 17]-code) | [i] | ✔ | |
| 19 | Linear OA(798, 16839, F7, 22) (dual of [16839, 16741, 23]-code) | [i] | ✔ | |
| 20 | Linear OA(773, 16839, F7, 16) (dual of [16839, 16766, 17]-code) | [i] | ✔ | |
| 21 | Linear OA(7107, 16848, F7, 23) (dual of [16848, 16741, 24]-code) | [i] | ✔ | |
| 22 | Linear OA(777, 16848, F7, 16) (dual of [16848, 16771, 17]-code) | [i] | ✔ | |
| 23 | Linear OA(778, 16854, F7, 16) (dual of [16854, 16776, 17]-code) | [i] | ✔ | |
| 24 | Linear OA(791, 16833, F7, 20) (dual of [16833, 16742, 21]-code) | [i] | ✔ | Construction XX with a Chain of Extended Narrow-Sense BCH Codes |
| 25 | Linear OA(778, 16820, F7, 18) (dual of [16820, 16742, 19]-code) | [i] | ✔ | |
| 26 | Linear OA(771, 16828, F7, 16) (dual of [16828, 16757, 17]-code) | [i] | ✔ | |