Information on Result #619805
Linear OA(25635, 65544, F256, 15) (dual of [65544, 65509, 16]-code), using construction X applied to C([0,7]) ⊂ C([1,7]) based on
- linear OA(25629, 65537, F256, 15) (dual of [65537, 65508, 16]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 2564−1, defining interval I = [0,7], and minimum distance d ≥ |{−7,−6,…,7}|+1 = 16 (BCH-bound) [i]
- linear OA(25628, 65537, F256, 8) (dual of [65537, 65509, 9]-code), using the narrow-sense BCH-code C(I) with length 65537 | 2564−1, defining interval I = [1,7], and minimum distance d ≥ |{−7,−5,−3,…,7}|+1 = 9 (BCH-bound) [i]
- linear OA(2566, 7, F256, 6) (dual of [7, 1, 7]-code or 7-arc in PG(5,256)), using
- dual of repetition code with length 7 [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(1670, 131088, F16, 15) (dual of [131088, 131018, 16]-code) | [i] | Trace Code | |
| 2 | Linear OOA(25635, 44186, F256, 2, 15) (dual of [(44186, 2), 88337, 16]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(25635, 44186, F256, 3, 15) (dual of [(44186, 3), 132523, 16]-NRT-code) | [i] | ||
| 4 | Linear OOA(25635, 44186, F256, 4, 15) (dual of [(44186, 4), 176709, 16]-NRT-code) | [i] | ||
| 5 | Linear OOA(25635, 44186, F256, 5, 15) (dual of [(44186, 5), 220895, 16]-NRT-code) | [i] | ||
| 6 | Linear OOA(25635, 44186, F256, 6, 15) (dual of [(44186, 6), 265081, 16]-NRT-code) | [i] | ||
| 7 | Digital (20, 35, 44186)-net over F256 | [i] | ||