Information on Result #2789878
Linear OOA(2215, 4100, F2, 4, 30) (dual of [(4100, 4), 16185, 31]-NRT-code), using 22 times duplication based on linear OOA(2213, 4100, F2, 4, 30) (dual of [(4100, 4), 16187, 31]-NRT-code), using
- OOA 4-folding [i] based on linear OA(2213, 16400, F2, 30) (dual of [16400, 16187, 31]-code), using
- 2 times code embedding in larger space [i] based on linear OA(2211, 16398, F2, 30) (dual of [16398, 16187, 31]-code), using
- 1 times truncation [i] based on linear OA(2212, 16399, F2, 31) (dual of [16399, 16187, 32]-code), using
- construction X applied to Ce(30) ⊂ Ce(28) [i] based on
- linear OA(2211, 16384, F2, 31) (dual of [16384, 16173, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 16383 = 214−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(2197, 16384, F2, 29) (dual of [16384, 16187, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 16383 = 214−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(21, 15, F2, 1) (dual of [15, 14, 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(30) ⊂ Ce(28) [i] based on
- 1 times truncation [i] based on linear OA(2212, 16399, F2, 31) (dual of [16399, 16187, 32]-code), using
- 2 times code embedding in larger space [i] based on linear OA(2211, 16398, F2, 30) (dual of [16398, 16187, 31]-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(2215, 3498, F2, 5, 30) (dual of [(3498, 5), 17275, 31]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(2215, 3498, F2, 6, 30) (dual of [(3498, 6), 20773, 31]-NRT-code) | [i] | ||
| 3 | Linear OOA(2215, 3498, F2, 7, 30) (dual of [(3498, 7), 24271, 31]-NRT-code) | [i] | ||
| 4 | Linear OOA(2215, 3498, F2, 8, 30) (dual of [(3498, 8), 27769, 31]-NRT-code) | [i] | ||
| 5 | Digital (185, 215, 3498)-net over F2 | [i] | ||