Information on Result #865809
Linear OOA(2745, 366, F27, 2, 23) (dual of [(366, 2), 687, 24]-NRT-code), using OOA 2-folding based on linear OA(2745, 732, F27, 23) (dual of [732, 687, 24]-code), using
- construction XX applied to C1 = C([727,20]), C2 = C([0,21]), C3 = C1 + C2 = C([0,20]), and C∩ = C1 ∩ C2 = C([727,21]) [i] based on
- linear OA(2743, 728, F27, 22) (dual of [728, 685, 23]-code), using the primitive BCH-code C(I) with length 728 = 272−1, defining interval I = {−1,0,…,20}, and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(2743, 728, F27, 22) (dual of [728, 685, 23]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 272−1, defining interval I = [0,21], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(2745, 728, F27, 23) (dual of [728, 683, 24]-code), using the primitive BCH-code C(I) with length 728 = 272−1, defining interval I = {−1,0,…,21}, and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(2741, 728, F27, 21) (dual of [728, 687, 22]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 272−1, defining interval I = [0,20], and designed minimum distance d ≥ |I|+1 = 22 [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(2756, 394, F27, 2, 23) (dual of [(394, 2), 732, 24]-NRT-code) | [i] | (u, u+v)-Construction for OOAs | |
| 2 | Linear OOA(2757, 404, F27, 2, 23) (dual of [(404, 2), 751, 24]-NRT-code) | [i] | ||
| 3 | Linear OOA(2758, 414, F27, 2, 23) (dual of [(414, 2), 770, 24]-NRT-code) | [i] | ||
| 4 | Linear OOA(2759, 418, F27, 2, 23) (dual of [(418, 2), 777, 24]-NRT-code) | [i] | ||
| 5 | Linear OOA(2760, 430, F27, 2, 23) (dual of [(430, 2), 800, 24]-NRT-code) | [i] | ||
| 6 | Linear OOA(2761, 434, F27, 2, 23) (dual of [(434, 2), 807, 24]-NRT-code) | [i] | ||
| 7 | Linear OOA(2762, 442, F27, 2, 23) (dual of [(442, 2), 822, 24]-NRT-code) | [i] | ||
| 8 | Linear OOA(2763, 448, F27, 2, 23) (dual of [(448, 2), 833, 24]-NRT-code) | [i] | ||
| 9 | Linear OOA(2764, 452, F27, 2, 23) (dual of [(452, 2), 840, 24]-NRT-code) | [i] | ||
| 10 | Linear OOA(2765, 462, F27, 2, 23) (dual of [(462, 2), 859, 24]-NRT-code) | [i] | ||
| 11 | Digital (22, 45, 366)-net over F27 | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |