Information on Result #699672
Linear OA(12840, 2097168, F128, 13) (dual of [2097168, 2097128, 14]-code), using construction X applied to C([0,6]) ⊂ C([0,4]) based on
- 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(12825, 2097153, F128, 9) (dual of [2097153, 2097128, 10]-code), using the expurgated narrow-sense BCH-code C(I) with length 2097153 | 1286−1, defining interval I = [0,4], and minimum distance d ≥ |{−4,−3,…,4}|+1 = 10 (BCH-bound) [i]
- linear OA(1283, 15, F128, 3) (dual of [15, 12, 4]-code or 15-arc in PG(2,128) or 15-cap in PG(2,128)), using
- discarding factors / shortening the dual code based on linear OA(1283, 128, F128, 3) (dual of [128, 125, 4]-code or 128-arc in PG(2,128) or 128-cap in PG(2,128)), using
- Reed–Solomon code RS(125,128) [i]
- discarding factors / shortening the dual code based on linear OA(1283, 128, F128, 3) (dual of [128, 125, 4]-code or 128-arc in PG(2,128) or 128-cap in PG(2,128)), 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(1670, 2097168, S16, 13) | [i] | Discarding Parts of the Base for OAs | |
| 2 | OA(3256, 2097168, S32, 13) | [i] | ||
| 3 | OA(6447, 2097168, S64, 13) | [i] | ||
| 4 | Linear OOA(12840, 1143473, F128, 2, 13) (dual of [(1143473, 2), 2286906, 14]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 5 | Linear OOA(12840, 1143473, F128, 3, 13) (dual of [(1143473, 3), 3430379, 14]-NRT-code) | [i] | ||
| 6 | Linear OOA(12840, 1143473, F128, 4, 13) (dual of [(1143473, 4), 4573852, 14]-NRT-code) | [i] | ||
| 7 | Digital (27, 40, 1143473)-net over F128 | [i] | ||
| 8 | Linear OOA(12840, 1048584, F128, 2, 13) (dual of [(1048584, 2), 2097128, 14]-NRT-code) | [i] | OOA Folding | |
| 9 | Linear OOA(12840, 699056, F128, 3, 13) (dual of [(699056, 3), 2097128, 14]-NRT-code) | [i] | ||
| 10 | Linear OOA(12840, 524292, F128, 4, 13) (dual of [(524292, 4), 2097128, 14]-NRT-code) | [i] | ||