Information on Result #865649
Linear OOA(2741, 366, F27, 2, 21) (dual of [(366, 2), 691, 22]-NRT-code), using OOA 2-folding based on linear OA(2741, 732, F27, 21) (dual of [732, 691, 22]-code), using
- construction XX applied to C1 = C([727,18]), C2 = C([0,19]), C3 = C1 + C2 = C([0,18]), and C∩ = C1 ∩ C2 = C([727,19]) [i] based on
- linear OA(2739, 728, F27, 20) (dual of [728, 689, 21]-code), using the primitive BCH-code C(I) with length 728 = 272−1, defining interval I = {−1,0,…,18}, and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(2739, 728, F27, 20) (dual of [728, 689, 21]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 272−1, defining interval I = [0,19], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(2741, 728, F27, 21) (dual of [728, 687, 22]-code), using the primitive BCH-code C(I) with length 728 = 272−1, defining interval I = {−1,0,…,19}, and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(2737, 728, F27, 19) (dual of [728, 691, 20]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 272−1, defining interval I = [0,18], and designed minimum distance d ≥ |I|+1 = 20 [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(2751, 394, F27, 2, 21) (dual of [(394, 2), 737, 22]-NRT-code) | [i] | (u, u+v)-Construction for OOAs | |
| 2 | Linear OOA(2752, 404, F27, 2, 21) (dual of [(404, 2), 756, 22]-NRT-code) | [i] | ||
| 3 | Linear OOA(2753, 414, F27, 2, 21) (dual of [(414, 2), 775, 22]-NRT-code) | [i] | ||
| 4 | Linear OOA(2754, 418, F27, 2, 21) (dual of [(418, 2), 782, 22]-NRT-code) | [i] | ||
| 5 | Linear OOA(2755, 430, F27, 2, 21) (dual of [(430, 2), 805, 22]-NRT-code) | [i] | ||
| 6 | Linear OOA(2756, 434, F27, 2, 21) (dual of [(434, 2), 812, 22]-NRT-code) | [i] | ||
| 7 | Linear OOA(2757, 442, F27, 2, 21) (dual of [(442, 2), 827, 22]-NRT-code) | [i] | ||
| 8 | Linear OOA(2758, 448, F27, 2, 21) (dual of [(448, 2), 838, 22]-NRT-code) | [i] | ||
| 9 | Digital (20, 41, 358)-net over F27 | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |