Information on Result #2479499
Linear OOA(2163, 1039, F2, 2, 28) (dual of [(1039, 2), 1915, 29]-NRT-code), using 21 times duplication based on linear OOA(2162, 1039, F2, 2, 28) (dual of [(1039, 2), 1916, 29]-NRT-code), using
- strength reduction [i] based on linear OOA(2162, 1039, F2, 2, 29) (dual of [(1039, 2), 1916, 30]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2162, 2078, F2, 29) (dual of [2078, 1916, 30]-code), using
- 1 times code embedding in larger space [i] based on linear OA(2161, 2077, F2, 29) (dual of [2077, 1916, 30]-code), using
- construction X applied to C([0,14]) ⊂ C([0,12]) [i] based on
- linear OA(2155, 2049, F2, 29) (dual of [2049, 1894, 30]-code), using the expurgated narrow-sense BCH-code C(I) with length 2049 | 222−1, defining interval I = [0,14], and minimum distance d ≥ |{−14,−13,…,14}|+1 = 30 (BCH-bound) [i]
- 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(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([0,14]) ⊂ C([0,12]) [i] based on
- 1 times code embedding in larger space [i] based on linear OA(2161, 2077, F2, 29) (dual of [2077, 1916, 30]-code), using
- OOA 2-folding [i] based on linear OA(2162, 2078, F2, 29) (dual of [2078, 1916, 30]-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(2163, 848, F2, 3, 28) (dual of [(848, 3), 2381, 29]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(2163, 848, F2, 4, 28) (dual of [(848, 4), 3229, 29]-NRT-code) | [i] | ||
| 3 | Linear OOA(2163, 848, F2, 5, 28) (dual of [(848, 5), 4077, 29]-NRT-code) | [i] | ||
| 4 | Linear OOA(2163, 848, F2, 6, 28) (dual of [(848, 6), 4925, 29]-NRT-code) | [i] | ||
| 5 | Linear OOA(2163, 848, F2, 7, 28) (dual of [(848, 7), 5773, 29]-NRT-code) | [i] | ||
| 6 | Linear OOA(2163, 848, F2, 8, 28) (dual of [(848, 8), 6621, 29]-NRT-code) | [i] | ||
| 7 | Digital (135, 163, 848)-net over F2 | [i] | ||