Information on Result #2479976
Linear OOA(2192, 1031, F2, 2, 34) (dual of [(1031, 2), 1870, 35]-NRT-code), using 21 times duplication based on linear OOA(2191, 1031, F2, 2, 34) (dual of [(1031, 2), 1871, 35]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(2189, 1030, F2, 2, 34) (dual of [(1030, 2), 1871, 35]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2189, 2060, F2, 34) (dual of [2060, 1871, 35]-code), using
- strength reduction [i] based on linear OA(2189, 2060, F2, 35) (dual of [2060, 1871, 36]-code), using
- construction X applied to Ce(34) ⊂ Ce(32) [i] based on
- linear OA(2188, 2048, F2, 35) (dual of [2048, 1860, 36]-code), using an extension Ce(34) of the primitive narrow-sense BCH-code C(I) with length 2047 = 211−1, defining interval I = [1,34], and designed minimum distance d ≥ |I|+1 = 35 [i]
- linear OA(2177, 2048, F2, 33) (dual of [2048, 1871, 34]-code), using an extension Ce(32) of the primitive narrow-sense BCH-code C(I) with length 2047 = 211−1, defining interval I = [1,32], and designed minimum distance d ≥ |I|+1 = 33 [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(34) ⊂ Ce(32) [i] based on
- strength reduction [i] based on linear OA(2189, 2060, F2, 35) (dual of [2060, 1871, 36]-code), using
- OOA 2-folding [i] based on linear OA(2189, 2060, F2, 34) (dual of [2060, 1871, 35]-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(2192, 825, F2, 3, 34) (dual of [(825, 3), 2283, 35]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(2192, 825, F2, 4, 34) (dual of [(825, 4), 3108, 35]-NRT-code) | [i] | ||
| 3 | Linear OOA(2192, 825, F2, 5, 34) (dual of [(825, 5), 3933, 35]-NRT-code) | [i] | ||
| 4 | Linear OOA(2192, 825, F2, 6, 34) (dual of [(825, 6), 4758, 35]-NRT-code) | [i] | ||
| 5 | Linear OOA(2192, 825, F2, 7, 34) (dual of [(825, 7), 5583, 35]-NRT-code) | [i] | ||
| 6 | Linear OOA(2192, 825, F2, 8, 34) (dual of [(825, 8), 6408, 35]-NRT-code) | [i] | ||
| 7 | Digital (158, 192, 825)-net over F2 | [i] | ||