Information on Result #1095818
Linear OOA(2186, 209721, F2, 5, 18) (dual of [(209721, 5), 1048419, 19]-NRT-code), using OOA 5-folding based on linear OA(2186, 1048605, F2, 18) (dual of [1048605, 1048419, 19]-code), using
- discarding factors / shortening the dual code based on linear OA(2186, 1048607, F2, 18) (dual of [1048607, 1048421, 19]-code), using
- 1 times truncation [i] based on linear OA(2187, 1048608, F2, 19) (dual of [1048608, 1048421, 20]-code), using
- construction X applied to Ce(18) ⊂ Ce(14) [i] based on
- linear OA(2181, 1048576, F2, 19) (dual of [1048576, 1048395, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 220−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(2141, 1048576, F2, 15) (dual of [1048576, 1048435, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 220−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(26, 32, F2, 3) (dual of [32, 26, 4]-code or 32-cap in PG(5,2)), using
- construction X applied to Ce(18) ⊂ Ce(14) [i] based on
- 1 times truncation [i] based on linear OA(2187, 1048608, F2, 19) (dual of [1048608, 1048421, 20]-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(2186, 183593, F2, 6, 18) (dual of [(183593, 6), 1101372, 19]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(2186, 183593, F2, 7, 18) (dual of [(183593, 7), 1284965, 19]-NRT-code) | [i] | ||
| 3 | Linear OOA(2186, 183593, F2, 8, 18) (dual of [(183593, 8), 1468558, 19]-NRT-code) | [i] | ||
| 4 | Digital (168, 186, 183593)-net over F2 | [i] | ||