Information on Result #1464553
Linear OOA(12840, 1143473, F128, 2, 13) (dual of [(1143473, 2), 2286906, 14]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OA(12840, 1143473, F128, 13) (dual of [1143473, 1143433, 14]-code), using
- discarding factors / shortening the dual code based on linear OA(12840, 2097168, F128, 13) (dual of [2097168, 2097128, 14]-code), using
- construction X applied to C([0,6]) ⊂ C([0,4]) [i] 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
- construction X applied to C([0,6]) ⊂ C([0,4]) [i] based on
Mode: 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 | OOA(6447, 1143473, S64, 2, 13) | [i] | Discarding Parts of the Base for OOAs | |
| 2 | Linear OOA(12840, 571736, F128, 4, 13) (dual of [(571736, 4), 2286904, 14]-NRT-code) | [i] | OOA Folding | |