Information on Result #879237
Linear OOA(12870, 8203, F128, 2, 32) (dual of [(8203, 2), 16336, 33]-NRT-code), using OOA 2-folding based on linear OA(12870, 16406, F128, 32) (dual of [16406, 16336, 33]-code), using
- discarding factors / shortening the dual code based on linear OA(12870, 16407, F128, 32) (dual of [16407, 16337, 33]-code), using
- construction X applied to Ce(31) ⊂ Ce(23) [i] based on
- linear OA(12863, 16384, F128, 32) (dual of [16384, 16321, 33]-code), using an extension Ce(31) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,31], and designed minimum distance d ≥ |I|+1 = 32 [i]
- linear OA(12847, 16384, F128, 24) (dual of [16384, 16337, 25]-code), using an extension Ce(23) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(1287, 23, F128, 7) (dual of [23, 16, 8]-code or 23-arc in PG(6,128)), using
- discarding factors / shortening the dual code based on linear OA(1287, 128, F128, 7) (dual of [128, 121, 8]-code or 128-arc in PG(6,128)), using
- Reed–Solomon code RS(121,128) [i]
- discarding factors / shortening the dual code based on linear OA(1287, 128, F128, 7) (dual of [128, 121, 8]-code or 128-arc in PG(6,128)), using
- construction X applied to Ce(31) ⊂ Ce(23) [i] based on
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(12870, 8010, F128, 3, 32) (dual of [(8010, 3), 23960, 33]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(12870, 8010, F128, 4, 32) (dual of [(8010, 4), 31970, 33]-NRT-code) | [i] | ||
| 3 | Digital (38, 70, 8010)-net over F128 | [i] | ||