Information on Result #866059
Linear OOA(2751, 366, F27, 2, 26) (dual of [(366, 2), 681, 27]-NRT-code), using OOA 2-folding based on linear OA(2751, 732, F27, 26) (dual of [732, 681, 27]-code), using
- construction XX applied to C1 = C([727,23]), C2 = C([0,24]), C3 = C1 + C2 = C([0,23]), and C∩ = C1 ∩ C2 = C([727,24]) [i] based on
- linear OA(2749, 728, F27, 25) (dual of [728, 679, 26]-code), using the primitive BCH-code C(I) with length 728 = 272−1, defining interval I = {−1,0,…,23}, and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(2749, 728, F27, 25) (dual of [728, 679, 26]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 272−1, defining interval I = [0,24], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(2751, 728, F27, 26) (dual of [728, 677, 27]-code), using the primitive BCH-code C(I) with length 728 = 272−1, defining interval I = {−1,0,…,24}, and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(2747, 728, F27, 24) (dual of [728, 681, 25]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 272−1, defining interval I = [0,23], and designed minimum distance d ≥ |I|+1 = 25 [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(2764, 394, F27, 2, 26) (dual of [(394, 2), 724, 27]-NRT-code) | [i] | (u, u+v)-Construction for OOAs | |
| 2 | Linear OOA(2765, 404, F27, 2, 26) (dual of [(404, 2), 743, 27]-NRT-code) | [i] | ||
| 3 | Linear OOA(2766, 414, F27, 2, 26) (dual of [(414, 2), 762, 27]-NRT-code) | [i] | ||
| 4 | Linear OOA(2767, 418, F27, 2, 26) (dual of [(418, 2), 769, 27]-NRT-code) | [i] | ||
| 5 | Linear OOA(2768, 430, F27, 2, 26) (dual of [(430, 2), 792, 27]-NRT-code) | [i] | ||
| 6 | Linear OOA(2769, 434, F27, 2, 26) (dual of [(434, 2), 799, 27]-NRT-code) | [i] | ||
| 7 | Linear OOA(2770, 442, F27, 2, 26) (dual of [(442, 2), 814, 27]-NRT-code) | [i] | ||
| 8 | Linear OOA(2771, 448, F27, 2, 26) (dual of [(448, 2), 825, 27]-NRT-code) | [i] | ||
| 9 | Linear OOA(2772, 450, F27, 2, 26) (dual of [(450, 2), 828, 27]-NRT-code) | [i] | ||
| 10 | Linear OOA(2773, 454, F27, 2, 26) (dual of [(454, 2), 835, 27]-NRT-code) | [i] | ||
| 11 | Linear OOA(2774, 462, F27, 2, 26) (dual of [(462, 2), 850, 27]-NRT-code) | [i] | ||
| 12 | Digital (25, 51, 366)-net over F27 | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |