Information on Result #1361830
Linear OOA(2239, 1055, F2, 2, 41) (dual of [(1055, 2), 1871, 42]-NRT-code), using OOA 2-folding based on linear OA(2239, 2110, F2, 41) (dual of [2110, 1871, 42]-code), using
- discarding factors / shortening the dual code based on linear OA(2239, 2111, F2, 41) (dual of [2111, 1872, 42]-code), using
- construction X applied to C([0,20]) ⊂ C([0,16]) [i] based on
- linear OA(2221, 2049, F2, 41) (dual of [2049, 1828, 42]-code), using the expurgated narrow-sense BCH-code C(I) with length 2049 | 222−1, defining interval I = [0,20], and minimum distance d ≥ |{−20,−19,…,20}|+1 = 42 (BCH-bound) [i]
- linear OA(2177, 2049, F2, 33) (dual of [2049, 1872, 34]-code), using the expurgated narrow-sense BCH-code C(I) with length 2049 | 222−1, defining interval I = [0,16], and minimum distance d ≥ |{−16,−15,…,16}|+1 = 34 (BCH-bound) [i]
- linear OA(218, 62, F2, 7) (dual of [62, 44, 8]-code), using
- discarding factors / shortening the dual code based on linear OA(218, 64, F2, 7) (dual of [64, 46, 8]-code), using
- adding a parity check bit [i] based on linear OA(217, 63, F2, 6) (dual of [63, 46, 7]-code), using
- a “cy†code from Brouwer’s database [i]
- adding a parity check bit [i] based on linear OA(217, 63, F2, 6) (dual of [63, 46, 7]-code), using
- discarding factors / shortening the dual code based on linear OA(218, 64, F2, 7) (dual of [64, 46, 8]-code), using
- construction X applied to C([0,20]) ⊂ C([0,16]) [i] based on
Mode: 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(2239, 1055, F2, 3, 41) (dual of [(1055, 3), 2926, 42]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(2239, 1055, F2, 4, 41) (dual of [(1055, 4), 3981, 42]-NRT-code) | [i] | ||
| 3 | Linear OOA(2239, 1055, F2, 5, 41) (dual of [(1055, 5), 5036, 42]-NRT-code) | [i] | ||
| 4 | Linear OOA(2239, 1055, F2, 6, 41) (dual of [(1055, 6), 6091, 42]-NRT-code) | [i] | ||
| 5 | Linear OOA(2239, 1055, F2, 7, 41) (dual of [(1055, 7), 7146, 42]-NRT-code) | [i] | ||
| 6 | Linear OOA(2239, 1055, F2, 8, 41) (dual of [(1055, 8), 8201, 42]-NRT-code) | [i] | ||
| 7 | Digital (198, 239, 1055)-net over F2 | [i] | ||