Information on Result #614313
Linear OA(757, 823543, F7, 10) (dual of [823543, 823486, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 823542 = 77−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10
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(762, 823551, F7, 10) (dual of [823551, 823489, 11]-code) | [i] | (u, u+v)-Construction | |
| 2 | Linear OA(763, 823554, F7, 10) (dual of [823554, 823491, 11]-code) | [i] | ||
| 3 | Linear OA(764, 823586, F7, 10) (dual of [823586, 823522, 11]-code) | [i] | ||
| 4 | Linear OOA(757, 516680, F7, 2, 10) (dual of [(516680, 2), 1033303, 11]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 5 | Linear OOA(757, 516680, F7, 3, 10) (dual of [(516680, 3), 1549983, 11]-NRT-code) | [i] | ||
| 6 | Digital (47, 57, 516680)-net over F7 | [i] | ||
| 7 | Linear OA(764, 823551, F7, 10) (dual of [823551, 823487, 11]-code) | [i] | (u, u−v, u+v+w)-Construction | |
| 8 | Linear OA(764, 823550, F7, 11) (dual of [823550, 823486, 12]-code) | [i] | ✔ | Construction X with Extended Narrow-Sense BCH Codes |
| 9 | Linear OA(757, 823550, F7, 10) (dual of [823550, 823493, 11]-code) | [i] | ✔ | |
| 10 | Linear OA(772, 823558, F7, 12) (dual of [823558, 823486, 13]-code) | [i] | ✔ | |
| 11 | Linear OA(758, 823558, F7, 10) (dual of [823558, 823500, 11]-code) | [i] | ✔ | |
| 12 | Linear OA(781, 823567, F7, 13) (dual of [823567, 823486, 14]-code) | [i] | ✔ | |
| 13 | Linear OA(761, 823568, F7, 10) (dual of [823568, 823507, 11]-code) | [i] | ✔ | |
| 14 | Linear OA(791, 823577, F7, 15) (dual of [823577, 823486, 16]-code) | [i] | ✔ | |
| 15 | Linear OA(789, 823575, F7, 14) (dual of [823575, 823486, 15]-code) | [i] | ✔ | |
| 16 | Linear OA(763, 823577, F7, 10) (dual of [823577, 823514, 11]-code) | [i] | ✔ | |
| 17 | Linear OA(799, 823585, F7, 16) (dual of [823585, 823486, 17]-code) | [i] | ✔ | |
| 18 | Linear OA(7110, 823593, F7, 17) (dual of [823593, 823483, 18]-code) | [i] | ✔ | |
| 19 | Linear OA(7110, 823595, F7, 17) (dual of [823595, 823485, 18]-code) | [i] | ✔ | |
| 20 | Linear OA(790, 823570, F7, 15) (dual of [823570, 823480, 16]-code) | [i] | ✔ | Construction XX with a Chain of Extended Narrow-Sense BCH Codes |
| 21 | Linear OA(762, 823570, F7, 10) (dual of [823570, 823508, 11]-code) | [i] | ✔ | |
| 22 | Linear OA(772, 823559, F7, 12) (dual of [823559, 823487, 13]-code) | [i] | ✔ | Construction X4 with Extended Narrow-Sense BCH Codes |
| 23 | Linear OA(758, 823559, F7, 10) (dual of [823559, 823501, 11]-code) | [i] | ✔ | |