Information on Result #691536
Linear OA(1632, 1048589, F16, 7) (dual of [1048589, 1048557, 8]-code), using construction X4 applied to C([0,3]) ⊂ C([0,2]) based on
- linear OA(1631, 1048577, F16, 7) (dual of [1048577, 1048546, 8]-code), using the expurgated narrow-sense BCH-code C(I) with length 1048577 | 1610−1, defining interval I = [0,3], and minimum distance d ≥ |{−3,−2,…,3}|+1 = 8 (BCH-bound) [i]
- linear OA(1621, 1048577, F16, 5) (dual of [1048577, 1048556, 6]-code), using the expurgated narrow-sense BCH-code C(I) with length 1048577 | 1610−1, defining interval I = [0,2], and minimum distance d ≥ |{−2,−1,0,1,2}|+1 = 6 (BCH-bound) [i]
- linear OA(1611, 12, F16, 11) (dual of [12, 1, 12]-code or 12-arc in PG(10,16)), using
- dual of repetition code with length 12 [i]
- linear OA(161, 12, F16, 1) (dual of [12, 11, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(161, 16, F16, 1) (dual of [16, 15, 2]-code), using
- Reed–Solomon code RS(15,16) [i]
- discarding factors / shortening the dual code based on linear OA(161, 16, F16, 1) (dual of [16, 15, 2]-code), 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(1632, 1048589, F16, 2, 7) (dual of [(1048589, 2), 2097146, 8]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Digital (25, 32, 1048589)-net over F16 | [i] | ||