Information on Result #906778
Linear OOA(2728, large, F27, 2, 5), using generalized (u, u+v)-construction based on
- linear OOA(271, 4194301, F27, 2, 1) (dual of [(4194301, 2), 8388601, 2]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(271, s, F27, 2, 1) for arbitrarily large s, using
- appending 1 arbitrary column [i] based on linear OA(271, s, F27, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- discarding factors / shortening the dual code based on linear OOA(271, s, F27, 2, 1) for arbitrarily large s, using
- linear OOA(276, 4194301, F27, 2, 2) (dual of [(4194301, 2), 8388596, 3]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(276, large, F27, 2, 2), using
- appending kth column [i] based on linear OA(276, large, F27, 2) (dual of [large, large−6, 3]-code), using
- Hamming code H(6,27) [i]
- appending kth column [i] based on linear OA(276, large, F27, 2) (dual of [large, large−6, 3]-code), using
- discarding factors / shortening the dual code based on linear OOA(276, large, F27, 2, 2), using
- linear OOA(2721, 4194301, F27, 2, 5) (dual of [(4194301, 2), 8388581, 6]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2721, 8388602, F27, 5) (dual of [8388602, 8388581, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(2721, large, F27, 5) (dual of [large, large−21, 6]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 14348908 | 2710−1, defining interval I = [0,2], and minimum distance d ≥ |{−2,−1,0,1,2}|+1 = 6 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(2721, large, F27, 5) (dual of [large, large−21, 6]-code), using
- OOA 2-folding [i] based on linear OA(2721, 8388602, F27, 5) (dual of [8388602, 8388581, 6]-code), using
Mode: Constructive and linear.
Optimality
Show details for fixed k and m, k and t, m 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(2728, large, F27, 2, 4) | [i] | Strength Reduction for OOAs | |
| 2 | Linear OOA(2728, large, F27, 2, 3) | [i] | ||
| 3 | Linear OOA(2730, large, F27, 2, 5) | [i] | NRT-Code Embedding in Larger Space | |
| 4 | Linear OOA(2732, large, F27, 2, 5) | [i] | ||
| 5 | Linear OOA(2734, large, F27, 2, 5) | [i] | ||
| 6 | Linear OOA(2736, large, F27, 2, 5) | [i] | ||
| 7 | Linear OOA(2738, large, F27, 2, 5) | [i] | ||
| 8 | Linear OOA(2740, large, F27, 2, 5) | [i] | ||
| 9 | Linear OOA(2742, large, F27, 2, 5) | [i] | ||
| 10 | Linear OOA(2744, large, F27, 2, 5) | [i] | ||
| 11 | Linear OOA(2746, large, F27, 2, 5) | [i] | ||
| 12 | Linear OOA(2748, large, F27, 2, 5) | [i] | ||
| 13 | Linear OOA(2750, large, F27, 2, 5) | [i] | ||
| 14 | Linear OOA(2752, large, F27, 2, 5) | [i] | ||
| 15 | Linear OOA(2754, large, F27, 2, 5) | [i] | ||
| 16 | Linear OOA(2756, large, F27, 2, 5) | [i] | ||
| 17 | Linear OOA(2758, large, F27, 2, 5) | [i] | ||
| 18 | Linear OOA(2760, large, F27, 2, 5) | [i] | ||
| 19 | Linear OOA(2762, large, F27, 2, 5) | [i] | ||
| 20 | Linear OOA(2764, large, F27, 2, 5) | [i] | ||
| 21 | Linear OOA(2766, large, F27, 2, 5) | [i] | ||
| 22 | Linear OOA(2768, large, F27, 2, 5) | [i] | ||
| 23 | Linear OOA(2770, large, F27, 2, 5) | [i] | ||
| 24 | Linear OOA(2772, large, F27, 2, 5) | [i] | ||
| 25 | Linear OOA(2774, large, F27, 2, 5) | [i] | ||
| 26 | Linear OOA(2776, large, F27, 2, 5) | [i] | ||
| 27 | Linear OOA(2778, large, F27, 2, 5) | [i] | ||
| 28 | Linear OOA(2780, large, F27, 2, 5) | [i] | ||
| 29 | Linear OOA(2782, large, F27, 2, 5) | [i] | ||
| 30 | Linear OOA(2784, large, F27, 2, 5) | [i] | ||
| 31 | Linear OOA(2786, large, F27, 2, 5) | [i] | ||
| 32 | Linear OOA(2788, large, F27, 2, 5) | [i] | ||
| 33 | Linear OOA(2790, large, F27, 2, 5) | [i] | ||
| 34 | Linear OOA(2792, large, F27, 2, 5) | [i] | ||
| 35 | Linear OOA(2794, large, F27, 2, 5) | [i] | ||
| 36 | Linear OOA(2796, large, F27, 2, 5) | [i] | ||
| 37 | Linear OOA(2798, large, F27, 2, 5) | [i] | ||
| 38 | Linear OOA(27100, large, F27, 2, 5) | [i] | ||
| 39 | Linear OOA(27102, large, F27, 2, 5) | [i] | ||
| 40 | Linear OOA(27104, large, F27, 2, 5) | [i] | ||
| 41 | Linear OOA(27106, large, F27, 2, 5) | [i] | ||
| 42 | Linear OOA(27108, large, F27, 2, 5) | [i] | ||
| 43 | Linear OOA(27110, large, F27, 2, 5) | [i] | ||
| 44 | Linear OOA(2729, large, F27, 2, 5) | [i] | OOA Duplication | |
| 45 | Linear OOA(2728, 8388602, F27, 6, 5) (dual of [(8388602, 6), 50331584, 6]-NRT-code) | [i] | OOA Stacking with Additional Row | |