Information on Result #691606
Linear OA(1647, 1048588, F16, 10) (dual of [1048588, 1048541, 11]-code), using construction X4 applied to Ce(9) ⊂ Ce(7) based on
- linear OA(1646, 1048576, F16, 10) (dual of [1048576, 1048530, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 165−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(1636, 1048576, F16, 8) (dual of [1048576, 1048540, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 165−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [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 OA(1654, 1048829, F16, 10) (dual of [1048829, 1048775, 11]-code) | [i] | (u, u+v)-Construction | |
| 2 | Linear OOA(1647, 1048588, F16, 2, 10) (dual of [(1048588, 2), 2097129, 11]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Digital (37, 47, 1048588)-net over F16 | [i] | ||
| 4 | Linear OOA(1647, 524294, F16, 2, 10) (dual of [(524294, 2), 1048541, 11]-NRT-code) | [i] | OOA Folding | |