Information on Result #1095420
Linear OOA(2160, 838867, F2, 5, 14) (dual of [(838867, 5), 4194175, 15]-NRT-code), using OOA 5-folding based on linear OA(2160, 4194335, F2, 14) (dual of [4194335, 4194175, 15]-code), using
- 1 times truncation [i] based on linear OA(2161, 4194336, F2, 15) (dual of [4194336, 4194175, 16]-code), using
- construction X applied to Ce(14) ⊂ Ce(10) [i] based on
- linear OA(2155, 4194304, F2, 15) (dual of [4194304, 4194149, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 222−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(2111, 4194304, F2, 11) (dual of [4194304, 4194193, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 222−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [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(14) ⊂ Ce(10) [i] based on
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(2222, 1677734, F2, 5, 14) (dual of [(1677734, 5), 8388448, 15]-NRT-code) | [i] | (u, u+v)-Construction for OOAs | |
| 2 | Linear OOA(2160, 838867, F2, 6, 14) (dual of [(838867, 6), 5033042, 15]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(2160, 838867, F2, 7, 14) (dual of [(838867, 7), 5871909, 15]-NRT-code) | [i] | ||
| 4 | Linear OOA(2160, 838867, F2, 8, 14) (dual of [(838867, 8), 6710776, 15]-NRT-code) | [i] | ||
| 5 | Digital (146, 160, 838867)-net over F2 | [i] | ||