Information on Result #866445
Linear OOA(2758, 366, F27, 2, 31) (dual of [(366, 2), 674, 32]-NRT-code), using OOA 2-folding based on linear OA(2758, 732, F27, 31) (dual of [732, 674, 32]-code), using
- construction XX applied to C1 = C([727,28]), C2 = C([0,29]), C3 = C1 + C2 = C([0,28]), and C∩ = C1 ∩ C2 = C([727,29]) [i] based on
- linear OA(2756, 728, F27, 30) (dual of [728, 672, 31]-code), using the primitive BCH-code C(I) with length 728 = 272−1, defining interval I = {−1,0,…,28}, and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(2756, 728, F27, 30) (dual of [728, 672, 31]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 272−1, defining interval I = [0,29], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(2758, 728, F27, 31) (dual of [728, 670, 32]-code), using the primitive BCH-code C(I) with length 728 = 272−1, defining interval I = {−1,0,…,29}, and designed minimum distance d ≥ |I|+1 = 32 [i]
- linear OA(2754, 728, F27, 29) (dual of [728, 674, 30]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 272−1, defining interval I = [0,28], and designed minimum distance d ≥ |I|+1 = 30 [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(2773, 394, F27, 2, 31) (dual of [(394, 2), 715, 32]-NRT-code) | [i] | (u, u+v)-Construction for OOAs | |
| 2 | Linear OOA(2774, 404, F27, 2, 31) (dual of [(404, 2), 734, 32]-NRT-code) | [i] | ||
| 3 | Linear OOA(2775, 414, F27, 2, 31) (dual of [(414, 2), 753, 32]-NRT-code) | [i] | ||
| 4 | Linear OOA(2776, 418, F27, 2, 31) (dual of [(418, 2), 760, 32]-NRT-code) | [i] | ||
| 5 | Linear OOA(2777, 430, F27, 2, 31) (dual of [(430, 2), 783, 32]-NRT-code) | [i] | ||
| 6 | Linear OOA(2778, 434, F27, 2, 31) (dual of [(434, 2), 790, 32]-NRT-code) | [i] | ||
| 7 | Linear OOA(2779, 442, F27, 2, 31) (dual of [(442, 2), 805, 32]-NRT-code) | [i] | ||
| 8 | Linear OOA(2780, 448, F27, 2, 31) (dual of [(448, 2), 816, 32]-NRT-code) | [i] | ||
| 9 | Linear OOA(2781, 450, F27, 2, 31) (dual of [(450, 2), 819, 32]-NRT-code) | [i] | ||
| 10 | Linear OOA(2782, 454, F27, 2, 31) (dual of [(454, 2), 826, 32]-NRT-code) | [i] | ||
| 11 | Linear OOA(2783, 460, F27, 2, 31) (dual of [(460, 2), 837, 32]-NRT-code) | [i] | ||
| 12 | Linear OOA(2784, 462, F27, 2, 31) (dual of [(462, 2), 840, 32]-NRT-code) | [i] | ||
| 13 | Linear OOA(2785, 468, F27, 2, 31) (dual of [(468, 2), 851, 32]-NRT-code) | [i] | ||
| 14 | OOA(2778, 448, S27, 2, 31) | [i] | ||
| 15 | Digital (27, 58, 303)-net over F27 | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |