Information on Result #879115
Linear OOA(12863, 8202, F128, 2, 29) (dual of [(8202, 2), 16341, 30]-NRT-code), using OOA 2-folding based on linear OA(12863, 16404, F128, 29) (dual of [16404, 16341, 30]-code), using
- construction X applied to Ce(28) ⊂ Ce(21) [i] based on
- linear OA(12857, 16384, F128, 29) (dual of [16384, 16327, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(12843, 16384, F128, 22) (dual of [16384, 16341, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(1286, 20, F128, 6) (dual of [20, 14, 7]-code or 20-arc in PG(5,128)), using
- discarding factors / shortening the dual code based on linear OA(1286, 128, F128, 6) (dual of [128, 122, 7]-code or 128-arc in PG(5,128)), using
- Reed–Solomon code RS(122,128) [i]
- discarding factors / shortening the dual code based on linear OA(1286, 128, F128, 6) (dual of [128, 122, 7]-code or 128-arc in PG(5,128)), 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(12863, 7288, F128, 3, 29) (dual of [(7288, 3), 21801, 30]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(12863, 7288, F128, 4, 29) (dual of [(7288, 4), 29089, 30]-NRT-code) | [i] | ||
| 3 | Digital (34, 63, 7288)-net over F128 | [i] | ||