Information on Result #1594584
Linear OOA(2191, 806, F2, 4, 34) (dual of [(806, 4), 3033, 35]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(2191, 806, F2, 2, 34) (dual of [(806, 2), 1421, 35]-NRT-code), using
- discarding factors / shortening the dual code 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
- 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
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(2191, 403, F2, 7, 34) (dual of [(403, 7), 2630, 35]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(2191, 403, F2, 8, 34) (dual of [(403, 8), 3033, 35]-NRT-code) | [i] | ||