Information on Result #1653573
Linear OOA(2182, 1677783, F2, 5, 15) (dual of [(1677783, 5), 8388733, 16]-NRT-code), using (u, u+v)-construction based on
- linear OOA(220, 63, F2, 5, 7) (dual of [(63, 5), 295, 8]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(220, 63, F2, 3, 7) (dual of [(63, 3), 169, 8]-NRT-code), using
- linear OOA(2162, 1677720, F2, 5, 15) (dual of [(1677720, 5), 8388438, 16]-NRT-code), using
- OOA 5-folding [i] based on linear OA(2162, 8388600, F2, 15) (dual of [8388600, 8388438, 16]-code), using
- discarding factors / shortening the dual code based on linear OA(2162, large, F2, 15) (dual of [large, large−162, 16]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 8388607 = 223−1, defining interval I = [0,14], and designed minimum distance d ≥ |I|+1 = 16 [i]
- discarding factors / shortening the dual code based on linear OA(2162, large, F2, 15) (dual of [large, large−162, 16]-code), using
- OOA 5-folding [i] based on linear OA(2162, 8388600, F2, 15) (dual of [8388600, 8388438, 16]-code), using
Mode: Linear.
Optimality
Show details for fixed k and m, k and s, k and t, m and s, m 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(2182, 1677783, F2, 6, 15) (dual of [(1677783, 6), 10066516, 16]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(2182, 1677783, F2, 7, 15) (dual of [(1677783, 7), 11744299, 16]-NRT-code) | [i] | ||
| 3 | Linear OOA(2182, 1677783, F2, 8, 15) (dual of [(1677783, 8), 13422082, 16]-NRT-code) | [i] | ||
| 4 | Digital (167, 182, 1677783)-net over F2 | [i] | ||