Information on Result #1052244
Linear OOA(2124, 2056, F2, 4, 19) (dual of [(2056, 4), 8100, 20]-NRT-code), using OOA 4-folding based on linear OA(2124, 8224, F2, 19) (dual of [8224, 8100, 20]-code), using
- construction X applied to Ce(18) ⊂ Ce(14) [i] based on
- linear OA(2118, 8192, F2, 19) (dual of [8192, 8074, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 8191 = 213−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(292, 8192, F2, 15) (dual of [8192, 8100, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 8191 = 213−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(26, 32, F2, 3) (dual of [32, 26, 4]-code or 32-cap in PG(5,2)), 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(2125, 2056, F2, 4, 19) (dual of [(2056, 4), 8099, 20]-NRT-code) | [i] | OOA Duplication | |
| 2 | Linear OOA(2126, 2056, F2, 4, 19) (dual of [(2056, 4), 8098, 20]-NRT-code) | [i] | ||
| 3 | Linear OOA(2124, 2056, F2, 5, 19) (dual of [(2056, 5), 10156, 20]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 4 | Linear OOA(2124, 2056, F2, 6, 19) (dual of [(2056, 6), 12212, 20]-NRT-code) | [i] | ||
| 5 | Linear OOA(2124, 2056, F2, 7, 19) (dual of [(2056, 7), 14268, 20]-NRT-code) | [i] | ||
| 6 | Linear OOA(2124, 2056, F2, 8, 19) (dual of [(2056, 8), 16324, 20]-NRT-code) | [i] | ||
| 7 | Digital (105, 124, 2056)-net over F2 | [i] | ||