Information on Result #1079846
Linear OOA(2178, 2097184, F2, 4, 14) (dual of [(2097184, 4), 8388558, 15]-NRT-code), using (u, u+v)-construction based on
- linear OOA(217, 34, F2, 4, 7) (dual of [(34, 4), 119, 8]-NRT-code), using
- extracting embedded OOA [i] based on digital (10, 17, 34)-net over F2, using
- linear OOA(2161, 2097150, F2, 4, 14) (dual of [(2097150, 4), 8388439, 15]-NRT-code), using
- OOA 4-folding [i] based on linear OA(2161, 8388600, F2, 14) (dual of [8388600, 8388439, 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 4-folding [i] based on linear OA(2161, 8388600, F2, 14) (dual of [8388600, 8388439, 15]-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(2246, 4194368, F2, 4, 14) (dual of [(4194368, 4), 16777226, 15]-NRT-code) | [i] | (u, u+v)-Construction for OOAs | |
| 2 | Linear OOA(2178, 2097184, F2, 5, 14) (dual of [(2097184, 5), 10485742, 15]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(2178, 2097184, F2, 6, 14) (dual of [(2097184, 6), 12582926, 15]-NRT-code) | [i] | ||
| 4 | Linear OOA(2178, 2097184, F2, 7, 14) (dual of [(2097184, 7), 14680110, 15]-NRT-code) | [i] | ||
| 5 | Linear OOA(2178, 2097184, F2, 8, 14) (dual of [(2097184, 8), 16777294, 15]-NRT-code) | [i] | ||
| 6 | Digital (164, 178, 2097184)-net over F2 | [i] | ||