Information on Result #614338
Linear OA(771, 823543, F7, 12) (dual of [823543, 823472, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 823542 = 77−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12
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(777, 823551, F7, 12) (dual of [823551, 823474, 13]-code) | [i] | (u, u+v)-Construction | |
| 2 | Linear OA(778, 823553, F7, 12) (dual of [823553, 823475, 13]-code) | [i] | ||
| 3 | Linear OA(779, 823561, F7, 12) (dual of [823561, 823482, 13]-code) | [i] | ||
| 4 | Linear OOA(771, 621595, F7, 2, 12) (dual of [(621595, 2), 1243119, 13]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 5 | Linear OOA(771, 621595, F7, 3, 12) (dual of [(621595, 3), 1864714, 13]-NRT-code) | [i] | ||
| 6 | Digital (59, 71, 621595)-net over F7 | [i] | ||
| 7 | Linear OA(780, 823553, F7, 12) (dual of [823553, 823473, 13]-code) | [i] | (u, u−v, u+v+w)-Construction | |
| 8 | Linear OA(778, 823550, F7, 13) (dual of [823550, 823472, 14]-code) | [i] | ✔ | Construction X with Extended Narrow-Sense BCH Codes |
| 9 | Linear OA(771, 823550, F7, 12) (dual of [823550, 823479, 13]-code) | [i] | ✔ | |
| 10 | Linear OA(786, 823558, F7, 14) (dual of [823558, 823472, 15]-code) | [i] | ✔ | |
| 11 | Linear OA(788, 823560, F7, 15) (dual of [823560, 823472, 16]-code) | [i] | ✔ | |
| 12 | Linear OA(772, 823558, F7, 12) (dual of [823558, 823486, 13]-code) | [i] | ✔ | |
| 13 | Linear OA(796, 823568, F7, 16) (dual of [823568, 823472, 17]-code) | [i] | ✔ | |
| 14 | Linear OA(774, 823567, F7, 12) (dual of [823567, 823493, 13]-code) | [i] | ✔ | |
| 15 | Linear OA(7105, 823577, F7, 17) (dual of [823577, 823472, 18]-code) | [i] | ✔ | |
| 16 | Linear OA(775, 823575, F7, 12) (dual of [823575, 823500, 13]-code) | [i] | ✔ | |
| 17 | Linear OA(778, 823585, F7, 12) (dual of [823585, 823507, 13]-code) | [i] | ✔ | |
| 18 | Linear OA(7104, 823570, F7, 17) (dual of [823570, 823466, 18]-code) | [i] | ✔ | Construction XX with a Chain of Extended Narrow-Sense BCH Codes |
| 19 | Linear OA(797, 823570, F7, 16) (dual of [823570, 823473, 17]-code) | [i] | ✔ | |
| 20 | Linear OA(787, 823553, F7, 15) (dual of [823553, 823466, 16]-code) | [i] | ✔ | |
| 21 | Linear OA(786, 823559, F7, 14) (dual of [823559, 823473, 15]-code) | [i] | ✔ | Construction X4 with Extended Narrow-Sense BCH Codes |
| 22 | Linear OA(772, 823559, F7, 12) (dual of [823559, 823487, 13]-code) | [i] | ✔ | |