Information on Result #865977
Linear OOA(2749, 366, F27, 2, 25) (dual of [(366, 2), 683, 26]-NRT-code), using OOA 2-folding based on linear OA(2749, 732, F27, 25) (dual of [732, 683, 26]-code), using
- construction XX applied to C1 = C([727,22]), C2 = C([0,23]), C3 = C1 + C2 = C([0,22]), and C∩ = C1 ∩ C2 = C([727,23]) [i] based on
- linear OA(2747, 728, F27, 24) (dual of [728, 681, 25]-code), using the primitive BCH-code C(I) with length 728 = 272−1, defining interval I = {−1,0,…,22}, and designed minimum distance d ≥ |I|+1 = 25 [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(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(2745, 728, F27, 23) (dual of [728, 683, 24]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 272−1, defining interval I = [0,22], and designed minimum distance d ≥ |I|+1 = 24 [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(2761, 394, F27, 2, 25) (dual of [(394, 2), 727, 26]-NRT-code) | [i] | (u, u+v)-Construction for OOAs | |
| 2 | Linear OOA(2762, 404, F27, 2, 25) (dual of [(404, 2), 746, 26]-NRT-code) | [i] | ||
| 3 | Linear OOA(2763, 414, F27, 2, 25) (dual of [(414, 2), 765, 26]-NRT-code) | [i] | ||
| 4 | Linear OOA(2764, 418, F27, 2, 25) (dual of [(418, 2), 772, 26]-NRT-code) | [i] | ||
| 5 | Linear OOA(2765, 430, F27, 2, 25) (dual of [(430, 2), 795, 26]-NRT-code) | [i] | ||
| 6 | Linear OOA(2766, 434, F27, 2, 25) (dual of [(434, 2), 802, 26]-NRT-code) | [i] | ||
| 7 | Linear OOA(2767, 442, F27, 2, 25) (dual of [(442, 2), 817, 26]-NRT-code) | [i] | ||
| 8 | Linear OOA(2768, 448, F27, 2, 25) (dual of [(448, 2), 828, 26]-NRT-code) | [i] | ||
| 9 | Linear OOA(2769, 450, F27, 2, 25) (dual of [(450, 2), 831, 26]-NRT-code) | [i] | ||
| 10 | Linear OOA(2770, 454, F27, 2, 25) (dual of [(454, 2), 838, 26]-NRT-code) | [i] | ||
| 11 | Linear OOA(2771, 462, F27, 2, 25) (dual of [(462, 2), 853, 26]-NRT-code) | [i] | ||
| 12 | Digital (24, 49, 366)-net over F27 | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |