Information on Result #2479818
Linear OOA(2185, 1039, F2, 2, 32) (dual of [(1039, 2), 1893, 33]-NRT-code), using 21 times duplication based on linear OOA(2184, 1039, F2, 2, 32) (dual of [(1039, 2), 1894, 33]-NRT-code), using
- strength reduction [i] based on linear OOA(2184, 1039, F2, 2, 33) (dual of [(1039, 2), 1894, 34]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2184, 2078, F2, 33) (dual of [2078, 1894, 34]-code), using
- 1 times code embedding in larger space [i] based on linear OA(2183, 2077, F2, 33) (dual of [2077, 1894, 34]-code), using
- construction X applied to C([0,16]) ⊂ C([0,14]) [i] based on
- linear OA(2177, 2049, F2, 33) (dual of [2049, 1872, 34]-code), using the expurgated narrow-sense BCH-code C(I) with length 2049 | 222−1, defining interval I = [0,16], and minimum distance d ≥ |{−16,−15,…,16}|+1 = 34 (BCH-bound) [i]
- linear OA(2155, 2049, F2, 29) (dual of [2049, 1894, 30]-code), using the expurgated narrow-sense BCH-code C(I) with length 2049 | 222−1, defining interval I = [0,14], and minimum distance d ≥ |{−14,−13,…,14}|+1 = 30 (BCH-bound) [i]
- linear OA(26, 28, F2, 3) (dual of [28, 22, 4]-code or 28-cap in PG(5,2)), using
- discarding factors / shortening the dual code based on linear OA(26, 32, F2, 3) (dual of [32, 26, 4]-code or 32-cap in PG(5,2)), using
- construction X applied to C([0,16]) ⊂ C([0,14]) [i] based on
- 1 times code embedding in larger space [i] based on linear OA(2183, 2077, F2, 33) (dual of [2077, 1894, 34]-code), using
- OOA 2-folding [i] based on linear OA(2184, 2078, F2, 33) (dual of [2078, 1894, 34]-code), using
Mode: Constructive and linear.
Optimality
Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n 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(2185, 885, F2, 3, 32) (dual of [(885, 3), 2470, 33]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(2185, 885, F2, 4, 32) (dual of [(885, 4), 3355, 33]-NRT-code) | [i] | ||
| 3 | Linear OOA(2185, 885, F2, 5, 32) (dual of [(885, 5), 4240, 33]-NRT-code) | [i] | ||
| 4 | Linear OOA(2185, 885, F2, 6, 32) (dual of [(885, 6), 5125, 33]-NRT-code) | [i] | ||
| 5 | Linear OOA(2185, 885, F2, 7, 32) (dual of [(885, 7), 6010, 33]-NRT-code) | [i] | ||
| 6 | Linear OOA(2185, 885, F2, 8, 32) (dual of [(885, 8), 6895, 33]-NRT-code) | [i] | ||
| 7 | Digital (153, 185, 885)-net over F2 | [i] | ||