Information on Result #2478515
Linear OOA(2247, large, F2, 2, 15), using 21 times duplication based on linear OOA(2246, large, F2, 2, 15), using
- 8 times NRT-code embedding in larger space [i] based on linear OOA(2230, 8388602, F2, 2, 15) (dual of [(8388602, 2), 16776974, 16]-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(2162, 4194301, F2, 2, 15) (dual of [(4194301, 2), 8388440, 16]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2162, 8388602, F2, 15) (dual of [8388602, 8388440, 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 2-folding [i] based on linear OA(2162, 8388602, F2, 15) (dual of [8388602, 8388440, 16]-code), using
- (u, u+v)-construction [i] based on
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(2247, 7402689, F2, 3, 15) (dual of [(7402689, 3), 22207820, 16]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(2247, 7402689, F2, 4, 15) (dual of [(7402689, 4), 29610509, 16]-NRT-code) | [i] | ||
| 3 | Linear OOA(2247, 7402689, F2, 5, 15) (dual of [(7402689, 5), 37013198, 16]-NRT-code) | [i] | ||
| 4 | Linear OOA(2247, 7402689, F2, 6, 15) (dual of [(7402689, 6), 44415887, 16]-NRT-code) | [i] | ||
| 5 | Linear OOA(2247, 7402689, F2, 7, 15) (dual of [(7402689, 7), 51818576, 16]-NRT-code) | [i] | ||
| 6 | Linear OOA(2247, 7402689, F2, 8, 15) (dual of [(7402689, 8), 59221265, 16]-NRT-code) | [i] | ||
| 7 | Digital (232, 247, 7402689)-net over F2 | [i] | ||