Information on Result #2480772
Linear OOA(2251, 1039, F2, 2, 44) (dual of [(1039, 2), 1827, 45]-NRT-code), using 21 times duplication based on linear OOA(2250, 1039, F2, 2, 44) (dual of [(1039, 2), 1828, 45]-NRT-code), using
- strength reduction [i] based on linear OOA(2250, 1039, F2, 2, 45) (dual of [(1039, 2), 1828, 46]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2250, 2078, F2, 45) (dual of [2078, 1828, 46]-code), using
- 1 times code embedding in larger space [i] based on linear OA(2249, 2077, F2, 45) (dual of [2077, 1828, 46]-code), using
- construction X applied to C([0,22]) ⊂ C([0,20]) [i] based on
- linear OA(2243, 2049, F2, 45) (dual of [2049, 1806, 46]-code), using the expurgated narrow-sense BCH-code C(I) with length 2049 | 222−1, defining interval I = [0,22], and minimum distance d ≥ |{−22,−21,…,22}|+1 = 46 (BCH-bound) [i]
- 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(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([0,22]) ⊂ C([0,20]) [i] based on
- 1 times code embedding in larger space [i] based on linear OA(2249, 2077, F2, 45) (dual of [2077, 1828, 46]-code), using
- OOA 2-folding [i] based on linear OA(2250, 2078, F2, 45) (dual of [2078, 1828, 46]-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(2251, 1028, F2, 3, 44) (dual of [(1028, 3), 2833, 45]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(2251, 1028, F2, 4, 44) (dual of [(1028, 4), 3861, 45]-NRT-code) | [i] | ||
| 3 | Linear OOA(2251, 1028, F2, 5, 44) (dual of [(1028, 5), 4889, 45]-NRT-code) | [i] | ||
| 4 | Linear OOA(2251, 1028, F2, 6, 44) (dual of [(1028, 6), 5917, 45]-NRT-code) | [i] | ||
| 5 | Linear OOA(2251, 1028, F2, 7, 44) (dual of [(1028, 7), 6945, 45]-NRT-code) | [i] | ||
| 6 | Linear OOA(2251, 1028, F2, 8, 44) (dual of [(1028, 8), 7973, 45]-NRT-code) | [i] | ||
| 7 | Digital (207, 251, 1028)-net over F2 | [i] | ||