Information on Result #1079964
Linear OOA(2190, 2097405, F2, 4, 15) (dual of [(2097405, 4), 8389430, 16]-NRT-code), using (u, u+v)-construction based on
- linear OOA(226, 254, F2, 4, 7) (dual of [(254, 4), 990, 8]-NRT-code), using
- OOA stacking with additional row [i] based on linear OOA(226, 255, F2, 3, 7) (dual of [(255, 3), 739, 8]-NRT-code), using
- linear OOA(2164, 2097151, F2, 4, 15) (dual of [(2097151, 4), 8388440, 16]-NRT-code), using
- OOA 2-folding [i] based on linear OOA(2164, 4194302, F2, 2, 15) (dual of [(4194302, 2), 8388440, 16]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on 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
- 1 times NRT-code embedding in larger space [i] based on linear OOA(2162, 4194301, F2, 2, 15) (dual of [(4194301, 2), 8388440, 16]-NRT-code), using
- OOA 2-folding [i] based on linear OOA(2164, 4194302, F2, 2, 15) (dual of [(4194302, 2), 8388440, 16]-NRT-code), using
Mode: Constructive and 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(2258, 4194810, F2, 4, 15) (dual of [(4194810, 4), 16778982, 16]-NRT-code) | [i] | (u, u+v)-Construction for OOAs | |
| 2 | Linear OOA(2190, 1799413, F2, 5, 15) (dual of [(1799413, 5), 8996875, 16]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(2190, 1799413, F2, 6, 15) (dual of [(1799413, 6), 10796288, 16]-NRT-code) | [i] | ||
| 4 | Linear OOA(2190, 1799413, F2, 7, 15) (dual of [(1799413, 7), 12595701, 16]-NRT-code) | [i] | ||
| 5 | Linear OOA(2190, 1799413, F2, 8, 15) (dual of [(1799413, 8), 14395114, 16]-NRT-code) | [i] | ||
| 6 | Digital (175, 190, 1799413)-net over F2 | [i] | ||