Information on Result #991379
Linear OOA(8158, 177148, F81, 3, 20) (dual of [(177148, 3), 531386, 21]-NRT-code), using OOA 3-folding based on linear OA(8158, 531444, F81, 20) (dual of [531444, 531386, 21]-code), using
- construction X applied to Ce(19) ⊂ Ce(18) [i] based on
- linear OA(8158, 531441, F81, 20) (dual of [531441, 531383, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 531440 = 813−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(8155, 531441, F81, 19) (dual of [531441, 531386, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 531440 = 813−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(810, 3, F81, 0) (dual of [3, 3, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(810, s, F81, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
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 OOA(8168, 177230, F81, 3, 20) (dual of [(177230, 3), 531622, 21]-NRT-code) | [i] | (u, u+v)-Construction for OOAs | |
| 2 | Linear OOA(8169, 177248, F81, 3, 20) (dual of [(177248, 3), 531675, 21]-NRT-code) | [i] | ||
| 3 | Linear OOA(8170, 177264, F81, 3, 20) (dual of [(177264, 3), 531722, 21]-NRT-code) | [i] | ||
| 4 | Linear OOA(8172, 177298, F81, 3, 20) (dual of [(177298, 3), 531822, 21]-NRT-code) | [i] | ||
| 5 | Linear OOA(8173, 177312, F81, 3, 20) (dual of [(177312, 3), 531863, 21]-NRT-code) | [i] | ||
| 6 | Linear OOA(8174, 177330, F81, 3, 20) (dual of [(177330, 3), 531916, 21]-NRT-code) | [i] | ||
| 7 | Linear OOA(8175, 177348, F81, 3, 20) (dual of [(177348, 3), 531969, 21]-NRT-code) | [i] | ||
| 8 | Linear OOA(8176, 177364, F81, 3, 20) (dual of [(177364, 3), 532016, 21]-NRT-code) | [i] | ||
| 9 | Linear OOA(8176, 177394, F81, 3, 20) (dual of [(177394, 3), 532106, 21]-NRT-code) | [i] | ||
| 10 | Linear OOA(8158, 177148, F81, 4, 20) (dual of [(177148, 4), 708534, 21]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 11 | Digital (38, 58, 177148)-net over F81 | [i] | ||