Information on Result #879276
Linear OOA(12872, 8204, F128, 2, 33) (dual of [(8204, 2), 16336, 34]-NRT-code), using OOA 2-folding based on linear OA(12872, 16408, F128, 33) (dual of [16408, 16336, 34]-code), using
- construction X applied to C([0,16]) ⊂ C([0,12]) [i] based on
- linear OA(12865, 16385, F128, 33) (dual of [16385, 16320, 34]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385 | 1284−1, defining interval I = [0,16], and minimum distance d ≥ |{−16,−15,…,16}|+1 = 34 (BCH-bound) [i]
- linear OA(12849, 16385, F128, 25) (dual of [16385, 16336, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385 | 1284−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [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
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(12872, 7817, F128, 3, 33) (dual of [(7817, 3), 23379, 34]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(12872, 7817, F128, 4, 33) (dual of [(7817, 4), 31196, 34]-NRT-code) | [i] | ||
| 3 | Digital (39, 72, 7817)-net over F128 | [i] | ||