Information on Result #1131838
Linear OOA(2181, 43693, F2, 6, 20) (dual of [(43693, 6), 261977, 21]-NRT-code), using OOA 6-folding based on linear OA(2181, 262158, F2, 20) (dual of [262158, 261977, 21]-code), using
- discarding factors / shortening the dual code based on linear OA(2181, 262162, F2, 20) (dual of [262162, 261981, 21]-code), using
- 1 times truncation [i] based on linear OA(2182, 262163, F2, 21) (dual of [262163, 261981, 22]-code), using
- construction X applied to Ce(20) ⊂ Ce(18) [i] based on
- linear OA(2181, 262144, F2, 21) (dual of [262144, 261963, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 262143 = 218−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(2163, 262144, F2, 19) (dual of [262144, 261981, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 262143 = 218−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(21, 19, F2, 1) (dual of [19, 18, 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(20) ⊂ Ce(18) [i] based on
- 1 times truncation [i] based on linear OA(2182, 262163, F2, 21) (dual of [262163, 261981, 22]-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(2181, 43693, F2, 7, 20) (dual of [(43693, 7), 305670, 21]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(2181, 43693, F2, 8, 20) (dual of [(43693, 8), 349363, 21]-NRT-code) | [i] | ||
| 3 | Digital (161, 181, 43693)-net over F2 | [i] | ||