Information on Result #947874
Linear OOA(2223, 1375, F2, 3, 37) (dual of [(1375, 3), 3902, 38]-NRT-code), using OOA 3-folding based on linear OA(2223, 4125, F2, 37) (dual of [4125, 3902, 38]-code), using
- discarding factors / shortening the dual code based on linear OA(2223, 4127, F2, 37) (dual of [4127, 3904, 38]-code), using
- construction X applied to C([0,18]) ⊂ C([0,16]) [i] based on
- 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(2193, 4097, F2, 33) (dual of [4097, 3904, 34]-code), using the expurgated narrow-sense BCH-code C(I) with length 4097 | 224−1, defining interval I = [0,16], and minimum distance d ≥ |{−16,−15,…,16}|+1 = 34 (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
- construction X applied to C([0,18]) ⊂ C([0,16]) [i] based on
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(2223, 1375, F2, 3, 36) (dual of [(1375, 3), 3902, 37]-NRT-code) | [i] | Strength Reduction for OOAs | |
| 2 | Linear OOA(2223, 1290, F2, 4, 37) (dual of [(1290, 4), 4937, 38]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(2223, 1290, F2, 5, 37) (dual of [(1290, 5), 6227, 38]-NRT-code) | [i] | ||
| 4 | Linear OOA(2223, 1290, F2, 6, 37) (dual of [(1290, 6), 7517, 38]-NRT-code) | [i] | ||
| 5 | Linear OOA(2223, 1290, F2, 7, 37) (dual of [(1290, 7), 8807, 38]-NRT-code) | [i] | ||
| 6 | Linear OOA(2223, 1290, F2, 8, 37) (dual of [(1290, 8), 10097, 38]-NRT-code) | [i] | ||
| 7 | Digital (186, 223, 1290)-net over F2 | [i] | ||