Information on Result #2789762
Linear OOA(2190, 2056, F2, 4, 29) (dual of [(2056, 4), 8034, 30]-NRT-code), using 21 times duplication based on linear OOA(2189, 2056, F2, 4, 29) (dual of [(2056, 4), 8035, 30]-NRT-code), using
- OOA 4-folding [i] based on linear OA(2189, 8224, F2, 29) (dual of [8224, 8035, 30]-code), using
- discarding factors / shortening the dual code based on linear OA(2189, 8225, F2, 29) (dual of [8225, 8036, 30]-code), using
- construction X applied to C([0,14]) ⊂ C([0,12]) [i] based on
- linear OA(2183, 8193, F2, 29) (dual of [8193, 8010, 30]-code), using the expurgated narrow-sense BCH-code C(I) with length 8193 | 226−1, defining interval I = [0,14], and minimum distance d ≥ |{−14,−13,…,14}|+1 = 30 (BCH-bound) [i]
- linear OA(2157, 8193, F2, 25) (dual of [8193, 8036, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 8193 | 226−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [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 C([0,14]) ⊂ C([0,12]) [i] based on
- discarding factors / shortening the dual code based on linear OA(2189, 8225, F2, 29) (dual of [8225, 8036, 30]-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(2190, 2056, F2, 5, 29) (dual of [(2056, 5), 10090, 30]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(2190, 2056, F2, 6, 29) (dual of [(2056, 6), 12146, 30]-NRT-code) | [i] | ||
| 3 | Linear OOA(2190, 2056, F2, 7, 29) (dual of [(2056, 7), 14202, 30]-NRT-code) | [i] | ||
| 4 | Linear OOA(2190, 2056, F2, 8, 29) (dual of [(2056, 8), 16258, 30]-NRT-code) | [i] | ||
| 5 | Digital (161, 190, 2056)-net over F2 | [i] | ||