Information on Result #2478386
Linear OOA(2231, large, F2, 2, 14), using 1 times NRT-code embedding in larger space based on linear OOA(2229, 8388602, F2, 2, 14) (dual of [(8388602, 2), 16776975, 15]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(268, 4194303, F2, 2, 7) (dual of [(4194303, 2), 8388538, 8]-NRT-code), using
- linear OOA(2161, 4194301, F2, 2, 14) (dual of [(4194301, 2), 8388441, 15]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2161, 8388602, F2, 14) (dual of [8388602, 8388441, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(2161, large, F2, 14) (dual of [large, large−161, 15]-code), using
- the primitive narrow-sense BCH-code C(I) with length 8388607 = 223−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- discarding factors / shortening the dual code based on linear OA(2161, large, F2, 14) (dual of [large, large−161, 15]-code), using
- OOA 2-folding [i] based on linear OA(2161, 8388602, F2, 14) (dual of [8388602, 8388441, 15]-code), using
Mode: Constructive and linear.
Optimality
Show details for fixed k and m, k and t, 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(2232, large, F2, 2, 14) | [i] | OOA Duplication | |
| 2 | Linear OOA(2231, large, F2, 3, 14) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(2231, large, F2, 4, 14) | [i] | ||
| 4 | Linear OOA(2231, large, F2, 5, 14) | [i] | ||
| 5 | Linear OOA(2231, large, F2, 6, 14) | [i] | ||
| 6 | Linear OOA(2231, large, F2, 7, 14) | [i] | ||
| 7 | Linear OOA(2231, large, F2, 8, 14) | [i] | ||
| 8 | Digital (217, 231, large)-net over F2 | [i] | ||