Information on Result #699670
Linear OA(12852, 2097168, F128, 17) (dual of [2097168, 2097116, 18]-code), using construction X applied to C([0,8]) ⊂ C([0,6]) based on
- linear OA(12849, 2097153, F128, 17) (dual of [2097153, 2097104, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 2097153 | 1286−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (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(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(3273, 2097168, S32, 17) | [i] | Discarding Parts of the Base for OAs | |
| 2 | OA(6461, 2097168, S64, 17) | [i] | ||
| 3 | Linear OOA(12852, 1048584, F128, 2, 17) (dual of [(1048584, 2), 2097116, 18]-NRT-code) | [i] | OOA Folding | |
| 4 | Linear OOA(12852, 699056, F128, 3, 17) (dual of [(699056, 3), 2097116, 18]-NRT-code) | [i] | ||
| 5 | Linear OOA(12852, 524292, F128, 4, 17) (dual of [(524292, 4), 2097116, 18]-NRT-code) | [i] | ||