Information on Result #1592431
Linear OOA(2158, 734, F2, 4, 28) (dual of [(734, 4), 2778, 29]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(2158, 734, F2, 2, 28) (dual of [(734, 2), 1310, 29]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2158, 1031, F2, 2, 28) (dual of [(1031, 2), 1904, 29]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(2156, 1030, F2, 2, 28) (dual of [(1030, 2), 1904, 29]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2156, 2060, F2, 28) (dual of [2060, 1904, 29]-code), using
- strength reduction [i] based on linear OA(2156, 2060, F2, 29) (dual of [2060, 1904, 30]-code), using
- construction X applied to Ce(28) ⊂ Ce(26) [i] based on
- linear OA(2155, 2048, F2, 29) (dual of [2048, 1893, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 2047 = 211−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(2144, 2048, F2, 27) (dual of [2048, 1904, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 2047 = 211−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(21, 12, F2, 1) (dual of [12, 11, 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
- strength reduction [i] based on linear OA(2156, 2060, F2, 29) (dual of [2060, 1904, 30]-code), using
- OOA 2-folding [i] based on linear OA(2156, 2060, F2, 28) (dual of [2060, 1904, 29]-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(2156, 1030, F2, 2, 28) (dual of [(1030, 2), 1904, 29]-NRT-code), using
Mode: 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(2158, 367, F2, 7, 28) (dual of [(367, 7), 2411, 29]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(2158, 367, F2, 8, 28) (dual of [(367, 8), 2778, 29]-NRT-code) | [i] | ||