Information on Result #619561
Linear OA(12825, 16390, F128, 11) (dual of [16390, 16365, 12]-code), using construction X applied to C([0,5]) ⊂ C([1,5]) based on
- linear OA(12821, 16385, F128, 11) (dual of [16385, 16364, 12]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385 | 1284−1, defining interval I = [0,5], and minimum distance d ≥ |{−5,−4,…,5}|+1 = 12 (BCH-bound) [i]
- linear OA(12820, 16385, F128, 6) (dual of [16385, 16365, 7]-code), using the narrow-sense BCH-code C(I) with length 16385 | 1284−1, defining interval I = [1,5], and minimum distance d ≥ |{−5,−3,−1,…,5}|+1 = 7 (BCH-bound) [i]
- linear OA(1284, 5, F128, 4) (dual of [5, 1, 5]-code or 5-arc in PG(3,128)), using
- dual of repetition code with length 5 [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(12825, 13585, F128, 2, 11) (dual of [(13585, 2), 27145, 12]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(12825, 13585, F128, 3, 11) (dual of [(13585, 3), 40730, 12]-NRT-code) | [i] | ||
| 3 | Linear OOA(12825, 13585, F128, 4, 11) (dual of [(13585, 4), 54315, 12]-NRT-code) | [i] | ||
| 4 | Digital (14, 25, 13585)-net over F128 | [i] | ||