Information on Result #2789049
Linear OOA(2159, 4100, F2, 4, 22) (dual of [(4100, 4), 16241, 23]-NRT-code), using 22 times duplication based on linear OOA(2157, 4100, F2, 4, 22) (dual of [(4100, 4), 16243, 23]-NRT-code), using
- OOA 4-folding [i] based on linear OA(2157, 16400, F2, 22) (dual of [16400, 16243, 23]-code), using
- 2 times code embedding in larger space [i] based on linear OA(2155, 16398, F2, 22) (dual of [16398, 16243, 23]-code), using
- 1 times truncation [i] based on linear OA(2156, 16399, F2, 23) (dual of [16399, 16243, 24]-code), using
- construction X applied to Ce(22) ⊂ Ce(20) [i] based on
- linear OA(2155, 16384, F2, 23) (dual of [16384, 16229, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 16383 = 214−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(2141, 16384, F2, 21) (dual of [16384, 16243, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 16383 = 214−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [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(22) ⊂ Ce(20) [i] based on
- 1 times truncation [i] based on linear OA(2156, 16399, F2, 23) (dual of [16399, 16243, 24]-code), using
- 2 times code embedding in larger space [i] based on linear OA(2155, 16398, F2, 22) (dual of [16398, 16243, 23]-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(2159, 3962, F2, 5, 22) (dual of [(3962, 5), 19651, 23]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(2159, 3962, F2, 6, 22) (dual of [(3962, 6), 23613, 23]-NRT-code) | [i] | ||
| 3 | Linear OOA(2159, 3962, F2, 7, 22) (dual of [(3962, 7), 27575, 23]-NRT-code) | [i] | ||
| 4 | Linear OOA(2159, 3962, F2, 8, 22) (dual of [(3962, 8), 31537, 23]-NRT-code) | [i] | ||
| 5 | Digital (137, 159, 3962)-net over F2 | [i] | ||