Information on Result #619531
Linear OA(12815, 16388, F128, 7) (dual of [16388, 16373, 8]-code), using construction X applied to C([0,3]) ⊂ C([1,3]) based on
- linear OA(12813, 16385, F128, 7) (dual of [16385, 16372, 8]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385 | 1284−1, defining interval I = [0,3], and minimum distance d ≥ |{−3,−2,…,3}|+1 = 8 (BCH-bound) [i]
- linear OA(12812, 16385, F128, 4) (dual of [16385, 16373, 5]-code), using the narrow-sense BCH-code C(I) with length 16385 | 1284−1, defining interval I = [1,3], and minimum distance d ≥ |{−3,−1,1,3}|+1 = 5 (BCH-bound) [i]
- linear OA(1282, 3, F128, 2) (dual of [3, 1, 3]-code or 3-arc in PG(1,128)), using
- dual of repetition code with length 3 [i]
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(12815, 16300, F128, 2, 7) (dual of [(16300, 2), 32585, 8]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(12815, 16300, F128, 3, 7) (dual of [(16300, 3), 48885, 8]-NRT-code) | [i] | ||
| 3 | Linear OOA(12815, 16300, F128, 4, 7) (dual of [(16300, 4), 65185, 8]-NRT-code) | [i] | ||
| 4 | Digital (8, 15, 16300)-net over F128 | [i] | ||