Information on Result #865393
Linear OOA(2749, 9843, F27, 2, 17) (dual of [(9843, 2), 19637, 18]-NRT-code), using OOA 2-folding based on linear OA(2749, 19686, F27, 17) (dual of [19686, 19637, 18]-code), using
- construction X applied to Ce(16) ⊂ Ce(15) [i] based on
- linear OA(2749, 19683, F27, 17) (dual of [19683, 19634, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 19682 = 273−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(2746, 19683, F27, 16) (dual of [19683, 19637, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 19682 = 273−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(270, 3, F27, 0) (dual of [3, 3, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(270, s, F27, 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(2757, 9871, F27, 2, 17) (dual of [(9871, 2), 19685, 18]-NRT-code) | [i] | (u, u+v)-Construction for OOAs | |
| 2 | Linear OOA(2758, 9881, F27, 2, 17) (dual of [(9881, 2), 19704, 18]-NRT-code) | [i] | ||
| 3 | Linear OOA(2759, 9891, F27, 2, 17) (dual of [(9891, 2), 19723, 18]-NRT-code) | [i] | ||
| 4 | Linear OOA(2760, 9895, F27, 2, 17) (dual of [(9895, 2), 19730, 18]-NRT-code) | [i] | ||
| 5 | Linear OOA(2761, 9907, F27, 2, 17) (dual of [(9907, 2), 19753, 18]-NRT-code) | [i] | ||
| 6 | Linear OOA(2762, 9911, F27, 2, 17) (dual of [(9911, 2), 19760, 18]-NRT-code) | [i] | ||
| 7 | OOA(2760, 9925, S27, 2, 17) | [i] | ||
| 8 | OOA(2761, 9943, S27, 2, 17) | [i] | ||
| 9 | OOA(2763, 9959, S27, 2, 17) | [i] | ||
| 10 | Digital (32, 49, 9843)-net over F27 | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |