Information on Result #878762
Linear OOA(12866, 1048588, F128, 2, 21) (dual of [(1048588, 2), 2097110, 22]-NRT-code), using OOA 2-folding based on linear OA(12866, 2097176, F128, 21) (dual of [2097176, 2097110, 22]-code), using
- construction X applied to C([0,10]) ⊂ C([0,7]) [i] based on
- linear OA(12861, 2097153, F128, 21) (dual of [2097153, 2097092, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 2097153 | 1286−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [i]
- 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(1285, 23, F128, 5) (dual of [23, 18, 6]-code or 23-arc in PG(4,128)), using
- discarding factors / shortening the dual code based on linear OA(1285, 128, F128, 5) (dual of [128, 123, 6]-code or 128-arc in PG(4,128)), using
- Reed–Solomon code RS(123,128) [i]
- discarding factors / shortening the dual code based on linear OA(1285, 128, F128, 5) (dual of [128, 123, 6]-code or 128-arc in PG(4,128)), 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(12866, 1048588, F128, 3, 21) (dual of [(1048588, 3), 3145698, 22]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(12866, 1048588, F128, 4, 21) (dual of [(1048588, 4), 4194286, 22]-NRT-code) | [i] | ||
| 3 | Digital (45, 66, 1048588)-net over F128 | [i] | ||