Information on Result #699674
Linear OA(12828, 2097168, F128, 9) (dual of [2097168, 2097140, 10]-code), using construction X applied to C([0,4]) ⊂ C([0,2]) based on
- 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(12813, 2097153, F128, 5) (dual of [2097153, 2097140, 6]-code), using the expurgated narrow-sense BCH-code C(I) with length 2097153 | 1286−1, defining interval I = [0,2], and minimum distance d ≥ |{−2,−1,0,1,2}|+1 = 6 (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 | Linear OOA(12828, 2097168, F128, 2, 9) (dual of [(2097168, 2), 4194308, 10]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(12828, 2097168, F128, 3, 9) (dual of [(2097168, 3), 6291476, 10]-NRT-code) | [i] | ||
| 3 | Linear OOA(12828, 2097168, F128, 4, 9) (dual of [(2097168, 4), 8388644, 10]-NRT-code) | [i] | ||
| 4 | Digital (19, 28, 2097168)-net over F128 | [i] | ||
| 5 | Linear OOA(12828, 1048584, F128, 2, 9) (dual of [(1048584, 2), 2097140, 10]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(12828, 699056, F128, 3, 9) (dual of [(699056, 3), 2097140, 10]-NRT-code) | [i] | ||
| 7 | Linear OOA(12828, 524292, F128, 4, 9) (dual of [(524292, 4), 2097140, 10]-NRT-code) | [i] | ||
| 8 | Linear OOA(12828, 524291, F128, 9, 9) (dual of [(524291, 9), 4718591, 10]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |