Information on Result #1152089
Linear OOA(2237, 37452, F2, 7, 27) (dual of [(37452, 7), 261927, 28]-NRT-code), using OOA 7-folding based on linear OA(2237, 262164, F2, 27) (dual of [262164, 261927, 28]-code), using
- 1 times code embedding in larger space [i] based on linear OA(2236, 262163, F2, 27) (dual of [262163, 261927, 28]-code), using
- construction X applied to Ce(26) ⊂ Ce(24) [i] based on
- 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(2217, 262144, F2, 25) (dual of [262144, 261927, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 262143 = 218−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [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(26) ⊂ Ce(24) [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(2238, 37452, F2, 7, 27) (dual of [(37452, 7), 261926, 28]-NRT-code) | [i] | OOA Duplication | |
| 2 | Linear OOA(2239, 37452, F2, 7, 27) (dual of [(37452, 7), 261925, 28]-NRT-code) | [i] | ||
| 3 | Linear OOA(2240, 37452, F2, 7, 27) (dual of [(37452, 7), 261924, 28]-NRT-code) | [i] | ||
| 4 | Linear OOA(2237, 34908, F2, 8, 27) (dual of [(34908, 8), 279027, 28]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 5 | Digital (210, 237, 34908)-net over F2 | [i] | ||