Information on Result #614350
Linear OA(756, 16807, F7, 13) (dual of [16807, 16751, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 16806 = 75−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13
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, 16815, F7, 13) (dual of [16815, 16753, 14]-code) | [i] | (u, u+v)-Construction | |
| 2 | Linear OA(763, 16817, F7, 13) (dual of [16817, 16754, 14]-code) | [i] | ||
| 3 | Linear OA(764, 16825, F7, 13) (dual of [16825, 16761, 14]-code) | [i] | ||
| 4 | Linear OA(766, 16833, F7, 13) (dual of [16833, 16767, 14]-code) | [i] | ||
| 5 | Linear OOA(756, 13745, F7, 2, 13) (dual of [(13745, 2), 27434, 14]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 6 | Linear OOA(756, 13745, F7, 3, 13) (dual of [(13745, 3), 41179, 14]-NRT-code) | [i] | ||
| 7 | Digital (43, 56, 13745)-net over F7 | [i] | ||
| 8 | Linear OA(765, 16817, F7, 13) (dual of [16817, 16752, 14]-code) | [i] | (u, u−v, u+v+w)-Construction | |
| 9 | Linear OA(766, 16823, F7, 13) (dual of [16823, 16757, 14]-code) | [i] | ||
| 10 | Linear OA(762, 16813, F7, 15) (dual of [16813, 16751, 16]-code) | [i] | ✔ | Construction X with Extended Narrow-Sense BCH Codes |
| 11 | Linear OA(756, 16812, F7, 13) (dual of [16812, 16756, 14]-code) | [i] | ✔ | |
| 12 | Linear OA(768, 16815, F7, 16) (dual of [16815, 16747, 17]-code) | [i] | ✔ | |
| 13 | Linear OA(769, 16820, F7, 16) (dual of [16820, 16751, 17]-code) | [i] | ✔ | |
| 14 | Linear OA(757, 16818, F7, 13) (dual of [16818, 16761, 14]-code) | [i] | ✔ | |
| 15 | Linear OA(775, 16826, F7, 17) (dual of [16826, 16751, 18]-code) | [i] | ✔ | |
| 16 | Linear OA(759, 16825, F7, 13) (dual of [16825, 16766, 14]-code) | [i] | ✔ | |
| 17 | Linear OA(782, 16833, F7, 18) (dual of [16833, 16751, 19]-code) | [i] | ✔ | |
| 18 | Linear OA(760, 16831, F7, 13) (dual of [16831, 16771, 14]-code) | [i] | ✔ | |
| 19 | Linear OA(788, 16839, F7, 19) (dual of [16839, 16751, 20]-code) | [i] | ✔ | |
| 20 | Linear OA(762, 16838, F7, 13) (dual of [16838, 16776, 14]-code) | [i] | ✔ | |
| 21 | Linear OA(797, 16848, F7, 20) (dual of [16848, 16751, 21]-code) | [i] | ✔ | |
| 22 | Linear OA(7104, 16855, F7, 22) (dual of [16855, 16751, 23]-code) | [i] | ✔ | |
| 23 | Linear OA(7110, 16857, F7, 23) (dual of [16857, 16747, 24]-code) | [i] | ✔ | |
| 24 | Linear OA(781, 16828, F7, 18) (dual of [16828, 16747, 19]-code) | [i] | ✔ | Construction XX with a Chain of Extended Narrow-Sense BCH Codes |
| 25 | Linear OA(776, 16828, F7, 17) (dual of [16828, 16752, 18]-code) | [i] | ✔ | |
| 26 | Linear OA(758, 16820, F7, 13) (dual of [16820, 16762, 14]-code) | [i] | ✔ | |
| 27 | Linear OA(761, 16833, F7, 13) (dual of [16833, 16772, 14]-code) | [i] | ✔ | |
| 28 | Linear OA(757, 16824, F7, 12) (dual of [16824, 16767, 13]-code) | [i] | ✔ | Construction X4 with Extended Narrow-Sense BCH Codes |
| 29 | Linear OOA(756, 2801, F7, 13, 13) (dual of [(2801, 13), 36357, 14]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |