Information on Result #699884
Linear OA(12868, 16420, F128, 29) (dual of [16420, 16352, 30]-code), using construction X applied to C([0,14]) ⊂ C([0,8]) based on
- linear OA(12857, 16385, F128, 29) (dual of [16385, 16328, 30]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385 | 1284−1, defining interval I = [0,14], and minimum distance d ≥ |{−14,−13,…,14}|+1 = 30 (BCH-bound) [i]
- linear OA(12833, 16385, F128, 17) (dual of [16385, 16352, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385 | 1284−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- linear OA(12811, 35, F128, 11) (dual of [35, 24, 12]-code or 35-arc in PG(10,128)), using
- discarding factors / shortening the dual code based on linear OA(12811, 128, F128, 11) (dual of [128, 117, 12]-code or 128-arc in PG(10,128)), using
- Reed–Solomon code RS(117,128) [i]
- discarding factors / shortening the dual code based on linear OA(12811, 128, F128, 11) (dual of [128, 117, 12]-code or 128-arc in PG(10,128)), 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(6480, 16420, S64, 29) | [i] | Discarding Parts of the Base for OAs | |
| 2 | Linear OOA(12868, 14562, F128, 2, 29) (dual of [(14562, 2), 29056, 30]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(12868, 14562, F128, 3, 29) (dual of [(14562, 3), 43618, 30]-NRT-code) | [i] | ||
| 4 | Linear OOA(12868, 14562, F128, 4, 29) (dual of [(14562, 4), 58180, 30]-NRT-code) | [i] | ||
| 5 | Digital (39, 68, 14562)-net over F128 | [i] | ||
| 6 | Linear OOA(12868, 8210, F128, 2, 29) (dual of [(8210, 2), 16352, 30]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(12868, 5473, F128, 3, 29) (dual of [(5473, 3), 16351, 30]-NRT-code) | [i] | ||
| 8 | Linear OOA(12868, 4105, F128, 4, 29) (dual of [(4105, 4), 16352, 30]-NRT-code) | [i] | ||