Information on Result #699657
Linear OA(12844, 2097160, F128, 15) (dual of [2097160, 2097116, 16]-code), using construction X applied to C([0,7]) ⊂ C([0,6]) based on
- linear OA(12843, 2097153, F128, 15) (dual of [2097153, 2097110, 16]-code), using the expurgated narrow-sense BCH-code C(I) with length 2097153 | 1286−1, defining interval I = [0,7], and minimum distance d ≥ |{−7,−6,…,7}|+1 = 16 (BCH-bound) [i]
- linear OA(12837, 2097153, F128, 13) (dual of [2097153, 2097116, 14]-code), using the expurgated narrow-sense BCH-code C(I) with length 2097153 | 1286−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
- linear OA(1281, 7, F128, 1) (dual of [7, 6, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(1281, s, F128, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
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 | OA(1677, 2097160, S16, 15) | [i] | Discarding Parts of the Base for OAs | |
| 2 | OA(3262, 2097160, S32, 15) | [i] | ||
| 3 | OA(6452, 2097160, S64, 15) | [i] | ||
| 4 | Linear OA(12852, 2097310, F128, 15) (dual of [2097310, 2097258, 16]-code) | [i] | (u, u+v)-Construction | |
| 5 | Linear OA(12855, 2097543, F128, 15) (dual of [2097543, 2097488, 16]-code) | [i] | ||
| 6 | Linear OOA(12844, 1048580, F128, 2, 15) (dual of [(1048580, 2), 2097116, 16]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(12844, 699053, F128, 3, 15) (dual of [(699053, 3), 2097115, 16]-NRT-code) | [i] | ||
| 8 | Linear OOA(12844, 524290, F128, 4, 15) (dual of [(524290, 4), 2097116, 16]-NRT-code) | [i] | ||
| 9 | Linear OOA(12844, 299594, F128, 15, 15) (dual of [(299594, 15), 4493866, 16]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |