Information on Result #1166168
Linear OOA(2245, 131075, F2, 8, 25) (dual of [(131075, 8), 1048355, 26]-NRT-code), using OOA 8-folding based on linear OA(2245, 1048600, F2, 25) (dual of [1048600, 1048355, 26]-code), using
- 3 times code embedding in larger space [i] based on linear OA(2242, 1048597, F2, 25) (dual of [1048597, 1048355, 26]-code), using
- construction X applied to Ce(24) ⊂ Ce(22) [i] based on
- linear OA(2241, 1048576, F2, 25) (dual of [1048576, 1048335, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 220−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(2221, 1048576, F2, 23) (dual of [1048576, 1048355, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 220−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(21, 21, F2, 1) (dual of [21, 20, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(21, s, F2, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X applied to Ce(24) ⊂ Ce(22) [i] based on
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(2246, 131075, F2, 8, 25) (dual of [(131075, 8), 1048354, 26]-NRT-code) | [i] | OOA Duplication | |
| 2 | Linear OOA(2244, 131074, F2, 8, 24) (dual of [(131074, 8), 1048348, 25]-NRT-code) | [i] | Truncation for OOAs | |
| 3 | Digital (220, 245, 131075)-net over F2 | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |