Information on Result #2961528
Linear OOA(2257, 37452, F2, 7, 29) (dual of [(37452, 7), 261907, 30]-NRT-code), using 22 times duplication based on linear OOA(2255, 37452, F2, 7, 29) (dual of [(37452, 7), 261909, 30]-NRT-code), using
- OOA 7-folding [i] based on linear OA(2255, 262164, F2, 29) (dual of [262164, 261909, 30]-code), using
- 1 times code embedding in larger space [i] based on linear OA(2254, 262163, F2, 29) (dual of [262163, 261909, 30]-code), using
- construction X applied to Ce(28) ⊂ Ce(26) [i] based on
- linear OA(2253, 262144, F2, 29) (dual of [262144, 261891, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 262143 = 218−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(2235, 262144, F2, 27) (dual of [262144, 261909, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 262143 = 218−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [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(28) ⊂ Ce(26) [i] based on
- 1 times code embedding in larger space [i] based on linear OA(2254, 262163, F2, 29) (dual of [262163, 261909, 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(2257, 33249, F2, 8, 29) (dual of [(33249, 8), 265735, 30]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Digital (228, 257, 33249)-net over F2 | [i] | ||