Information on Result #2480492
Linear OOA(2257, 2074, F2, 2, 40) (dual of [(2074, 2), 3891, 41]-NRT-code), using 2 times NRT-code embedding in larger space based on linear OOA(2253, 2072, F2, 2, 40) (dual of [(2072, 2), 3891, 41]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2253, 4144, F2, 40) (dual of [4144, 3891, 41]-code), using
- strength reduction [i] based on linear OA(2253, 4144, F2, 41) (dual of [4144, 3891, 42]-code), using
- construction X applied to Ce(40) ⊂ Ce(34) [i] based on
- linear OA(2241, 4096, F2, 41) (dual of [4096, 3855, 42]-code), using an extension Ce(40) of the primitive narrow-sense BCH-code C(I) with length 4095 = 212−1, defining interval I = [1,40], and designed minimum distance d ≥ |I|+1 = 41 [i]
- linear OA(2205, 4096, F2, 35) (dual of [4096, 3891, 36]-code), using an extension Ce(34) of the primitive narrow-sense BCH-code C(I) with length 4095 = 212−1, defining interval I = [1,34], and designed minimum distance d ≥ |I|+1 = 35 [i]
- linear OA(212, 48, F2, 5) (dual of [48, 36, 6]-code), using
- adding a parity check bit [i] based on linear OA(211, 47, F2, 4) (dual of [47, 36, 5]-code), using
- extracting embedded orthogonal array [i] based on digital (7, 11, 47)-net over F2, using
- adding a parity check bit [i] based on linear OA(211, 47, F2, 4) (dual of [47, 36, 5]-code), using
- construction X applied to Ce(40) ⊂ Ce(34) [i] based on
- strength reduction [i] based on linear OA(2253, 4144, F2, 41) (dual of [4144, 3891, 42]-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(2258, 2074, F2, 2, 40) (dual of [(2074, 2), 3890, 41]-NRT-code) | [i] | OOA Duplication | |
| 2 | Linear OOA(2257, 1686, F2, 3, 40) (dual of [(1686, 3), 4801, 41]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(2257, 1686, F2, 4, 40) (dual of [(1686, 4), 6487, 41]-NRT-code) | [i] | ||
| 4 | Linear OOA(2257, 1686, F2, 5, 40) (dual of [(1686, 5), 8173, 41]-NRT-code) | [i] | ||
| 5 | Linear OOA(2257, 1686, F2, 6, 40) (dual of [(1686, 6), 9859, 41]-NRT-code) | [i] | ||
| 6 | Linear OOA(2257, 1686, F2, 7, 40) (dual of [(1686, 7), 11545, 41]-NRT-code) | [i] | ||
| 7 | Linear OOA(2257, 1686, F2, 8, 40) (dual of [(1686, 8), 13231, 41]-NRT-code) | [i] | ||
| 8 | Digital (217, 257, 1686)-net over F2 | [i] | ||