Information on Result #866805
Linear OOA(2768, 366, F27, 2, 36) (dual of [(366, 2), 664, 37]-NRT-code), using OOA 2-folding based on linear OA(2768, 732, F27, 36) (dual of [732, 664, 37]-code), using
- construction XX applied to C1 = C([727,33]), C2 = C([0,34]), C3 = C1 + C2 = C([0,33]), and C∩ = C1 ∩ C2 = C([727,34]) [i] based on
- linear OA(2766, 728, F27, 35) (dual of [728, 662, 36]-code), using the primitive BCH-code C(I) with length 728 = 272−1, defining interval I = {−1,0,…,33}, and designed minimum distance d ≥ |I|+1 = 36 [i]
- linear OA(2766, 728, F27, 35) (dual of [728, 662, 36]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 272−1, defining interval I = [0,34], and designed minimum distance d ≥ |I|+1 = 36 [i]
- linear OA(2768, 728, F27, 36) (dual of [728, 660, 37]-code), using the primitive BCH-code C(I) with length 728 = 272−1, defining interval I = {−1,0,…,34}, and designed minimum distance d ≥ |I|+1 = 37 [i]
- linear OA(2764, 728, F27, 34) (dual of [728, 664, 35]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 272−1, defining interval I = [0,33], and designed minimum distance d ≥ |I|+1 = 35 [i]
- linear OA(270, 2, F27, 0) (dual of [2, 2, 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
- linear OA(270, 2, F27, 0) (dual of [2, 2, 1]-code) (see above)
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(2786, 394, F27, 2, 36) (dual of [(394, 2), 702, 37]-NRT-code) | [i] | (u, u+v)-Construction for OOAs | |
| 2 | Linear OOA(2787, 404, F27, 2, 36) (dual of [(404, 2), 721, 37]-NRT-code) | [i] | ||
| 3 | Linear OOA(2788, 414, F27, 2, 36) (dual of [(414, 2), 740, 37]-NRT-code) | [i] | ||
| 4 | Linear OOA(2789, 418, F27, 2, 36) (dual of [(418, 2), 747, 37]-NRT-code) | [i] | ||
| 5 | Linear OOA(2790, 430, F27, 2, 36) (dual of [(430, 2), 770, 37]-NRT-code) | [i] | ||
| 6 | Linear OOA(2791, 434, F27, 2, 36) (dual of [(434, 2), 777, 37]-NRT-code) | [i] | ||
| 7 | Linear OOA(2792, 442, F27, 2, 36) (dual of [(442, 2), 792, 37]-NRT-code) | [i] | ||
| 8 | Linear OOA(2793, 448, F27, 2, 36) (dual of [(448, 2), 803, 37]-NRT-code) | [i] | ||
| 9 | Linear OOA(2794, 450, F27, 2, 36) (dual of [(450, 2), 806, 37]-NRT-code) | [i] | ||
| 10 | Linear OOA(2795, 454, F27, 2, 36) (dual of [(454, 2), 813, 37]-NRT-code) | [i] | ||
| 11 | Linear OOA(2796, 460, F27, 2, 36) (dual of [(460, 2), 824, 37]-NRT-code) | [i] | ||
| 12 | Linear OOA(2797, 462, F27, 2, 36) (dual of [(462, 2), 827, 37]-NRT-code) | [i] | ||
| 13 | Linear OOA(27100, 468, F27, 2, 36) (dual of [(468, 2), 836, 37]-NRT-code) | [i] | ||
| 14 | Linear OOA(27101, 478, F27, 2, 36) (dual of [(478, 2), 855, 37]-NRT-code) | [i] | ||
| 15 | Digital (32, 68, 353)-net over F27 | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |