Information on Result #614304
Linear OA(743, 117649, F7, 9) (dual of [117649, 117606, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 117648 = 76−1, 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(747, 117657, F7, 9) (dual of [117657, 117610, 10]-code) | [i] | (u, u+v)-Construction | |
| 2 | Linear OA(748, 117660, F7, 9) (dual of [117660, 117612, 10]-code) | [i] | ||
| 3 | Linear OA(749, 117691, F7, 9) (dual of [117691, 117642, 10]-code) | [i] | ||
| 4 | Linear OOA(743, 66272, F7, 2, 9) (dual of [(66272, 2), 132501, 10]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 5 | Linear OOA(743, 66272, F7, 3, 9) (dual of [(66272, 3), 198773, 10]-NRT-code) | [i] | ||
| 6 | Digital (34, 43, 66272)-net over F7 | [i] | ||
| 7 | Linear OA(749, 117655, F7, 10) (dual of [117655, 117606, 11]-code) | [i] | ✔ | Construction X with Extended Narrow-Sense BCH Codes |
| 8 | Linear OA(743, 117655, F7, 9) (dual of [117655, 117612, 10]-code) | [i] | ✔ | |
| 9 | Linear OA(756, 117662, F7, 11) (dual of [117662, 117606, 12]-code) | [i] | ✔ | |
| 10 | Linear OA(746, 117664, F7, 9) (dual of [117664, 117618, 10]-code) | [i] | ✔ | |
| 11 | Linear OA(764, 117670, F7, 12) (dual of [117670, 117606, 13]-code) | [i] | ✔ | |
| 12 | Linear OA(747, 117671, F7, 9) (dual of [117671, 117624, 10]-code) | [i] | ✔ | |
| 13 | Linear OA(771, 117677, F7, 13) (dual of [117677, 117606, 14]-code) | [i] | ✔ | |
| 14 | Linear OA(780, 117686, F7, 15) (dual of [117686, 117606, 16]-code) | [i] | ✔ | |
| 15 | Linear OA(790, 117696, F7, 16) (dual of [117696, 117606, 17]-code) | [i] | ✔ | |
| 16 | Linear OA(778, 117679, F7, 14) (dual of [117679, 117601, 15]-code) | [i] | ✔ | Construction XX with a Chain of Extended Narrow-Sense BCH Codes |
| 17 | Linear OA(772, 117679, F7, 13) (dual of [117679, 117607, 14]-code) | [i] | ✔ | |
| 18 | Linear OA(745, 117658, F7, 9) (dual of [117658, 117613, 10]-code) | [i] | ✔ | |
| 19 | Linear OA(748, 117673, F7, 9) (dual of [117673, 117625, 10]-code) | [i] | ✔ | |
| 20 | Linear OA(756, 117663, F7, 11) (dual of [117663, 117607, 12]-code) | [i] | ✔ | Construction X4 with Extended Narrow-Sense BCH Codes |