Information on Result #672795
Linear OA(2247, 4127, F2, 41) (dual of [4127, 3880, 42]-code), using construction X applied to C([0,20]) ⊂ C([0,18]) based on
- linear OA(2241, 4097, F2, 41) (dual of [4097, 3856, 42]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097 | 224−1, defining interval I = [0,20], and minimum distance d ≥ |{−20,−19,…,20}|+1 = 42 (BCH-bound) [i]
- linear OA(2217, 4097, F2, 37) (dual of [4097, 3880, 38]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097 | 224−1, defining interval I = [0,18], and minimum distance d ≥ |{−18,−17,…,18}|+1 = 38 (BCH-bound) [i]
- linear OA(26, 30, F2, 3) (dual of [30, 24, 4]-code or 30-cap in PG(5,2)), using
- discarding factors / shortening the dual code based on 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 OA(2247, 4127, F2, 40) (dual of [4127, 3880, 41]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(2248, 4128, F2, 41) (dual of [4128, 3880, 42]-code) | [i] | Code Embedding in Larger Space | |
| 3 | Linear OA(2249, 4129, F2, 41) (dual of [4129, 3880, 42]-code) | [i] | ||
| 4 | Linear OA(2250, 4130, F2, 41) (dual of [4130, 3880, 42]-code) | [i] | ||
| 5 | Linear OA(2251, 4131, F2, 41) (dual of [4131, 3880, 42]-code) | [i] | ||
| 6 | Linear OA(2252, 4132, F2, 41) (dual of [4132, 3880, 42]-code) | [i] | ||
| 7 | Linear OA(2246, 4126, F2, 40) (dual of [4126, 3880, 41]-code) | [i] | Truncation | |
| 8 | Linear OOA(2247, 2063, F2, 2, 41) (dual of [(2063, 2), 3879, 42]-NRT-code) | [i] | OOA Folding | |
| 9 | Linear OOA(2247, 1375, F2, 3, 41) (dual of [(1375, 3), 3878, 42]-NRT-code) | [i] | ||
| 10 | Linear OOA(2247, 1031, F2, 4, 41) (dual of [(1031, 4), 3877, 42]-NRT-code) | [i] | ||
| 11 | Linear OOA(2247, 825, F2, 5, 41) (dual of [(825, 5), 3878, 42]-NRT-code) | [i] | ||
| 12 | Linear OOA(2247, 687, F2, 6, 41) (dual of [(687, 6), 3875, 42]-NRT-code) | [i] | ||
| 13 | Linear OOA(2247, 589, F2, 7, 41) (dual of [(589, 7), 3876, 42]-NRT-code) | [i] | ||
| 14 | Linear OOA(2247, 515, F2, 8, 41) (dual of [(515, 8), 3873, 42]-NRT-code) | [i] | ||