Information on Result #866591
Linear OOA(2762, 366, F27, 2, 33) (dual of [(366, 2), 670, 34]-NRT-code), using OOA 2-folding based on linear OA(2762, 732, F27, 33) (dual of [732, 670, 34]-code), using
- construction XX applied to C1 = C([727,30]), C2 = C([0,31]), C3 = C1 + C2 = C([0,30]), and C∩ = C1 ∩ C2 = C([727,31]) [i] based on
- linear OA(2760, 728, F27, 32) (dual of [728, 668, 33]-code), using the primitive BCH-code C(I) with length 728 = 272−1, defining interval I = {−1,0,…,30}, and designed minimum distance d ≥ |I|+1 = 33 [i]
- linear OA(2760, 728, F27, 32) (dual of [728, 668, 33]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 272−1, defining interval I = [0,31], and designed minimum distance d ≥ |I|+1 = 33 [i]
- linear OA(2762, 728, F27, 33) (dual of [728, 666, 34]-code), using the primitive BCH-code C(I) with length 728 = 272−1, defining interval I = {−1,0,…,31}, and designed minimum distance d ≥ |I|+1 = 34 [i]
- linear OA(2758, 728, F27, 31) (dual of [728, 670, 32]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 272−1, defining interval I = [0,30], and designed minimum distance d ≥ |I|+1 = 32 [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(2778, 394, F27, 2, 33) (dual of [(394, 2), 710, 34]-NRT-code) | [i] | (u, u+v)-Construction for OOAs | |
| 2 | Linear OOA(2779, 404, F27, 2, 33) (dual of [(404, 2), 729, 34]-NRT-code) | [i] | ||
| 3 | Linear OOA(2780, 414, F27, 2, 33) (dual of [(414, 2), 748, 34]-NRT-code) | [i] | ||
| 4 | Linear OOA(2781, 418, F27, 2, 33) (dual of [(418, 2), 755, 34]-NRT-code) | [i] | ||
| 5 | Linear OOA(2782, 430, F27, 2, 33) (dual of [(430, 2), 778, 34]-NRT-code) | [i] | ||
| 6 | Linear OOA(2783, 434, F27, 2, 33) (dual of [(434, 2), 785, 34]-NRT-code) | [i] | ||
| 7 | Linear OOA(2784, 442, F27, 2, 33) (dual of [(442, 2), 800, 34]-NRT-code) | [i] | ||
| 8 | Linear OOA(2785, 448, F27, 2, 33) (dual of [(448, 2), 811, 34]-NRT-code) | [i] | ||
| 9 | Linear OOA(2786, 450, F27, 2, 33) (dual of [(450, 2), 814, 34]-NRT-code) | [i] | ||
| 10 | Linear OOA(2787, 454, F27, 2, 33) (dual of [(454, 2), 821, 34]-NRT-code) | [i] | ||
| 11 | Linear OOA(2788, 460, F27, 2, 33) (dual of [(460, 2), 832, 34]-NRT-code) | [i] | ||
| 12 | Linear OOA(2789, 462, F27, 2, 33) (dual of [(462, 2), 835, 34]-NRT-code) | [i] | ||
| 13 | Linear OOA(2791, 468, F27, 2, 33) (dual of [(468, 2), 845, 34]-NRT-code) | [i] | ||
| 14 | Digital (29, 62, 323)-net over F27 | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |