Information on Result #991516
Linear OOA(8167, 177148, F81, 3, 23) (dual of [(177148, 3), 531377, 24]-NRT-code), using OOA 3-folding based on linear OA(8167, 531444, F81, 23) (dual of [531444, 531377, 24]-code), using
- construction X applied to Ce(22) ⊂ Ce(21) [i] based on
- linear OA(8167, 531441, F81, 23) (dual of [531441, 531374, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 531440 = 813−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(8164, 531441, F81, 22) (dual of [531441, 531377, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 531440 = 813−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [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(8178, 177230, F81, 3, 23) (dual of [(177230, 3), 531612, 24]-NRT-code) | [i] | (u, u+v)-Construction for OOAs | |
| 2 | Linear OOA(8179, 177248, F81, 3, 23) (dual of [(177248, 3), 531665, 24]-NRT-code) | [i] | ||
| 3 | Linear OOA(8180, 177264, F81, 3, 23) (dual of [(177264, 3), 531712, 24]-NRT-code) | [i] | ||
| 4 | Linear OOA(8182, 177298, F81, 3, 23) (dual of [(177298, 3), 531812, 24]-NRT-code) | [i] | ||
| 5 | Linear OOA(8167, 177148, F81, 4, 23) (dual of [(177148, 4), 708525, 24]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 6 | Digital (44, 67, 177148)-net over F81 | [i] | ||