Information on Result #1166492
Linear OOA(2254, 32770, F2, 8, 29) (dual of [(32770, 8), 261906, 30]-NRT-code), using OOA 8-folding based on linear OA(2254, 262160, F2, 29) (dual of [262160, 261906, 30]-code), using
- discarding factors / shortening the dual code 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
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(2254, 32770, F2, 8, 28) (dual of [(32770, 8), 261906, 29]-NRT-code) | [i] | Strength Reduction for OOAs | |
| 2 | Linear OOA(2255, 32770, F2, 8, 29) (dual of [(32770, 8), 261905, 30]-NRT-code) | [i] | OOA Duplication | |
| 3 | Linear OOA(2256, 32770, F2, 8, 29) (dual of [(32770, 8), 261904, 30]-NRT-code) | [i] | ||
| 4 | Linear OOA(2257, 32770, F2, 8, 29) (dual of [(32770, 8), 261903, 30]-NRT-code) | [i] | ||
| 5 | Linear OOA(2258, 32770, F2, 8, 29) (dual of [(32770, 8), 261902, 30]-NRT-code) | [i] | ||
| 6 | Digital (225, 254, 32770)-net over F2 | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |