Information on Result #2480478
Linear OOA(2229, 1039, F2, 2, 40) (dual of [(1039, 2), 1849, 41]-NRT-code), using 21 times duplication based on linear OOA(2228, 1039, F2, 2, 40) (dual of [(1039, 2), 1850, 41]-NRT-code), using
- strength reduction [i] based on linear OOA(2228, 1039, F2, 2, 41) (dual of [(1039, 2), 1850, 42]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2228, 2078, F2, 41) (dual of [2078, 1850, 42]-code), using
- 1 times code embedding in larger space [i] based on linear OA(2227, 2077, F2, 41) (dual of [2077, 1850, 42]-code), using
- construction X applied to C([0,20]) ⊂ C([0,18]) [i] based on
- linear OA(2221, 2049, F2, 41) (dual of [2049, 1828, 42]-code), using the expurgated narrow-sense BCH-code C(I) with length 2049 | 222−1, defining interval I = [0,20], and minimum distance d ≥ |{−20,−19,…,20}|+1 = 42 (BCH-bound) [i]
- linear OA(2199, 2049, F2, 37) (dual of [2049, 1850, 38]-code), using the expurgated narrow-sense BCH-code C(I) with length 2049 | 222−1, defining interval I = [0,18], and minimum distance d ≥ |{−18,−17,…,18}|+1 = 38 (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([0,20]) ⊂ C([0,18]) [i] based on
- 1 times code embedding in larger space [i] based on linear OA(2227, 2077, F2, 41) (dual of [2077, 1850, 42]-code), using
- OOA 2-folding [i] based on linear OA(2228, 2078, F2, 41) (dual of [2078, 1850, 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(2229, 977, F2, 3, 40) (dual of [(977, 3), 2702, 41]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(2229, 977, F2, 4, 40) (dual of [(977, 4), 3679, 41]-NRT-code) | [i] | ||
| 3 | Linear OOA(2229, 977, F2, 5, 40) (dual of [(977, 5), 4656, 41]-NRT-code) | [i] | ||
| 4 | Linear OOA(2229, 977, F2, 6, 40) (dual of [(977, 6), 5633, 41]-NRT-code) | [i] | ||
| 5 | Linear OOA(2229, 977, F2, 7, 40) (dual of [(977, 7), 6610, 41]-NRT-code) | [i] | ||
| 6 | Linear OOA(2229, 977, F2, 8, 40) (dual of [(977, 8), 7587, 41]-NRT-code) | [i] | ||
| 7 | Digital (189, 229, 977)-net over F2 | [i] | ||