Information on Result #2480068
Linear OOA(2196, 1039, F2, 2, 35) (dual of [(1039, 2), 1882, 36]-NRT-code), using 1 times NRT-code embedding in larger space based on linear OOA(2194, 1038, F2, 2, 35) (dual of [(1038, 2), 1882, 36]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2194, 2076, F2, 35) (dual of [2076, 1882, 36]-code), using
- construction X applied to Ce(34) ⊂ Ce(30) [i] based on
- linear OA(2188, 2048, F2, 35) (dual of [2048, 1860, 36]-code), using an extension Ce(34) of the primitive narrow-sense BCH-code C(I) with length 2047 = 211−1, defining interval I = [1,34], and designed minimum distance d ≥ |I|+1 = 35 [i]
- linear OA(2166, 2048, F2, 31) (dual of [2048, 1882, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 2047 = 211−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [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 Ce(34) ⊂ Ce(30) [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(2197, 1039, F2, 2, 35) (dual of [(1039, 2), 1881, 36]-NRT-code) | [i] | OOA Duplication | |
| 2 | Linear OOA(2196, 809, F2, 3, 35) (dual of [(809, 3), 2231, 36]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(2196, 809, F2, 4, 35) (dual of [(809, 4), 3040, 36]-NRT-code) | [i] | ||
| 4 | Linear OOA(2196, 809, F2, 5, 35) (dual of [(809, 5), 3849, 36]-NRT-code) | [i] | ||
| 5 | Linear OOA(2196, 809, F2, 6, 35) (dual of [(809, 6), 4658, 36]-NRT-code) | [i] | ||
| 6 | Linear OOA(2196, 809, F2, 7, 35) (dual of [(809, 7), 5467, 36]-NRT-code) | [i] | ||
| 7 | Linear OOA(2196, 809, F2, 8, 35) (dual of [(809, 8), 6276, 36]-NRT-code) | [i] | ||
| 8 | Digital (161, 196, 809)-net over F2 | [i] | ||