Information on Result #1052646
Linear OOA(2160, 4103, F2, 4, 22) (dual of [(4103, 4), 16252, 23]-NRT-code), using OOA 4-folding based on linear OA(2160, 16412, F2, 22) (dual of [16412, 16252, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(2160, 16415, F2, 22) (dual of [16415, 16255, 23]-code), using
- 1 times truncation [i] based on linear OA(2161, 16416, F2, 23) (dual of [16416, 16255, 24]-code), using
- construction X applied to Ce(22) ⊂ Ce(18) [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(2127, 16384, F2, 19) (dual of [16384, 16257, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 16383 = 214−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(26, 32, F2, 3) (dual of [32, 26, 4]-code or 32-cap in PG(5,2)), using
- construction X applied to Ce(22) ⊂ Ce(18) [i] based on
- 1 times truncation [i] based on linear OA(2161, 16416, F2, 23) (dual of [16416, 16255, 24]-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(2160, 4103, F2, 5, 22) (dual of [(4103, 5), 20355, 23]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(2160, 4103, F2, 6, 22) (dual of [(4103, 6), 24458, 23]-NRT-code) | [i] | ||
| 3 | Linear OOA(2160, 4103, F2, 7, 22) (dual of [(4103, 7), 28561, 23]-NRT-code) | [i] | ||
| 4 | Linear OOA(2160, 4103, F2, 8, 22) (dual of [(4103, 8), 32664, 23]-NRT-code) | [i] | ||
| 5 | Digital (138, 160, 4103)-net over F2 | [i] | ||