Information on Result #619787
Linear OA(25625, 65542, F256, 11) (dual of [65542, 65517, 12]-code), using construction X applied to C([0,5]) ⊂ C([1,5]) based on
- linear OA(25621, 65537, F256, 11) (dual of [65537, 65516, 12]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 2564−1, defining interval I = [0,5], and minimum distance d ≥ |{−5,−4,…,5}|+1 = 12 (BCH-bound) [i]
- linear OA(25620, 65537, F256, 6) (dual of [65537, 65517, 7]-code), using the narrow-sense BCH-code C(I) with length 65537 | 2564−1, defining interval I = [1,5], and minimum distance d ≥ |{−5,−3,−1,…,5}|+1 = 7 (BCH-bound) [i]
- linear OA(2564, 5, F256, 4) (dual of [5, 1, 5]-code or 5-arc in PG(3,256)), 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 OA(1650, 131084, F16, 11) (dual of [131084, 131034, 12]-code) | [i] | Trace Code | |
| 2 | Linear OOA(25625, 42968, F256, 2, 11) (dual of [(42968, 2), 85911, 12]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(25625, 42968, F256, 3, 11) (dual of [(42968, 3), 128879, 12]-NRT-code) | [i] | ||
| 4 | Linear OOA(25625, 42968, F256, 4, 11) (dual of [(42968, 4), 171847, 12]-NRT-code) | [i] | ||
| 5 | Linear OOA(25625, 42968, F256, 5, 11) (dual of [(42968, 5), 214815, 12]-NRT-code) | [i] | ||
| 6 | Linear OOA(25625, 42968, F256, 6, 11) (dual of [(42968, 6), 257783, 12]-NRT-code) | [i] | ||
| 7 | Digital (14, 25, 42968)-net over F256 | [i] | ||