Information on Result #1756933
Digital (186, 222, 1375)-net over F2, using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(2222, 1375, F2, 3, 36) (dual of [(1375, 3), 3903, 37]-NRT-code), using
- OOA 3-folding [i] based on linear OA(2222, 4125, F2, 36) (dual of [4125, 3903, 37]-code), using
- discarding factors / shortening the dual code based on linear OA(2222, 4126, F2, 36) (dual of [4126, 3904, 37]-code), using
- 1 times truncation [i] 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
- 1 times truncation [i] based on linear OA(2223, 4127, F2, 37) (dual of [4127, 3904, 38]-code), using
- discarding factors / shortening the dual code based on linear OA(2222, 4126, F2, 36) (dual of [4126, 3904, 37]-code), using
Mode: Linear.
Optimality
Show details for fixed k and m, k and s, k and t, m and s, m and t, t and s.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Digital (187, 223, 1375)-net over F2 | [i] | Net Duplication | |