Information on Result #2479146
Linear OOA(2141, 1039, F2, 2, 24) (dual of [(1039, 2), 1937, 25]-NRT-code), using 21 times duplication based on linear OOA(2140, 1039, F2, 2, 24) (dual of [(1039, 2), 1938, 25]-NRT-code), using
- strength reduction [i] based on linear OOA(2140, 1039, F2, 2, 25) (dual of [(1039, 2), 1938, 26]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2140, 2078, F2, 25) (dual of [2078, 1938, 26]-code), using
- 1 times code embedding in larger space [i] based on linear OA(2139, 2077, F2, 25) (dual of [2077, 1938, 26]-code), using
- construction X applied to C([0,12]) ⊂ C([0,10]) [i] based on
- linear OA(2133, 2049, F2, 25) (dual of [2049, 1916, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 2049 | 222−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
- linear OA(2111, 2049, F2, 21) (dual of [2049, 1938, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 2049 | 222−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (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([0,12]) ⊂ C([0,10]) [i] based on
- 1 times code embedding in larger space [i] based on linear OA(2139, 2077, F2, 25) (dual of [2077, 1938, 26]-code), using
- OOA 2-folding [i] based on linear OA(2140, 2078, F2, 25) (dual of [2078, 1938, 26]-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(2141, 823, F2, 3, 24) (dual of [(823, 3), 2328, 25]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(2141, 823, F2, 4, 24) (dual of [(823, 4), 3151, 25]-NRT-code) | [i] | ||
| 3 | Linear OOA(2141, 823, F2, 5, 24) (dual of [(823, 5), 3974, 25]-NRT-code) | [i] | ||
| 4 | Linear OOA(2141, 823, F2, 6, 24) (dual of [(823, 6), 4797, 25]-NRT-code) | [i] | ||
| 5 | Linear OOA(2141, 823, F2, 7, 24) (dual of [(823, 7), 5620, 25]-NRT-code) | [i] | ||
| 6 | Linear OOA(2141, 823, F2, 8, 24) (dual of [(823, 8), 6443, 25]-NRT-code) | [i] | ||
| 7 | Digital (117, 141, 823)-net over F2 | [i] | ||