Information on Result #991424
Linear OOA(8161, 177148, F81, 3, 21) (dual of [(177148, 3), 531383, 22]-NRT-code), using OOA 3-folding based on linear OA(8161, 531444, F81, 21) (dual of [531444, 531383, 22]-code), using
- construction X applied to Ce(20) ⊂ Ce(19) [i] based on
- linear OA(8161, 531441, F81, 21) (dual of [531441, 531380, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 531440 = 813−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- 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(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(8171, 177230, F81, 3, 21) (dual of [(177230, 3), 531619, 22]-NRT-code) | [i] | (u, u+v)-Construction for OOAs | |
| 2 | Linear OOA(8172, 177248, F81, 3, 21) (dual of [(177248, 3), 531672, 22]-NRT-code) | [i] | ||
| 3 | Linear OOA(8173, 177264, F81, 3, 21) (dual of [(177264, 3), 531719, 22]-NRT-code) | [i] | ||
| 4 | Linear OOA(8175, 177298, F81, 3, 21) (dual of [(177298, 3), 531819, 22]-NRT-code) | [i] | ||
| 5 | Linear OOA(8176, 177312, F81, 3, 21) (dual of [(177312, 3), 531860, 22]-NRT-code) | [i] | ||
| 6 | Linear OOA(8177, 177330, F81, 3, 21) (dual of [(177330, 3), 531913, 22]-NRT-code) | [i] | ||
| 7 | Linear OOA(8178, 177348, F81, 3, 21) (dual of [(177348, 3), 531966, 22]-NRT-code) | [i] | ||
| 8 | Linear OOA(8179, 177364, F81, 3, 21) (dual of [(177364, 3), 532013, 22]-NRT-code) | [i] | ||
| 9 | Linear OOA(8179, 177394, F81, 3, 21) (dual of [(177394, 3), 532103, 22]-NRT-code) | [i] | ||
| 10 | Linear OOA(8161, 177148, F81, 4, 21) (dual of [(177148, 4), 708531, 22]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 11 | Digital (40, 61, 177148)-net over F81 | [i] | ||