Information on Result #1054301
Linear OOA(2244, 2057, F2, 4, 37) (dual of [(2057, 4), 7984, 38]-NRT-code), using OOA 4-folding based on linear OA(2244, 8228, F2, 37) (dual of [8228, 7984, 38]-code), using
- 3 times code embedding in larger space [i] based on linear OA(2241, 8225, F2, 37) (dual of [8225, 7984, 38]-code), using
- construction X applied to C([0,18]) ⊂ C([0,16]) [i] based on
- linear OA(2235, 8193, F2, 37) (dual of [8193, 7958, 38]-code), using the expurgated narrow-sense BCH-code C(I) with length 8193 | 226−1, defining interval I = [0,18], and minimum distance d ≥ |{−18,−17,…,18}|+1 = 38 (BCH-bound) [i]
- linear OA(2209, 8193, F2, 33) (dual of [8193, 7984, 34]-code), using the expurgated narrow-sense BCH-code C(I) with length 8193 | 226−1, defining interval I = [0,16], and minimum distance d ≥ |{−16,−15,…,16}|+1 = 34 (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([0,18]) ⊂ 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(2244, 2057, F2, 4, 36) (dual of [(2057, 4), 7984, 37]-NRT-code) | [i] | Strength Reduction for OOAs | |
| 2 | Linear OOA(2245, 2057, F2, 4, 37) (dual of [(2057, 4), 7983, 38]-NRT-code) | [i] | OOA Duplication | |
| 3 | Linear OOA(2246, 2057, F2, 4, 37) (dual of [(2057, 4), 7982, 38]-NRT-code) | [i] | ||
| 4 | Linear OOA(2243, 2056, F2, 4, 36) (dual of [(2056, 4), 7981, 37]-NRT-code) | [i] | Truncation for OOAs | |
| 5 | Linear OOA(2244, 2057, F2, 5, 37) (dual of [(2057, 5), 10041, 38]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 6 | Linear OOA(2244, 2057, F2, 6, 37) (dual of [(2057, 6), 12098, 38]-NRT-code) | [i] | ||
| 7 | Linear OOA(2244, 2057, F2, 7, 37) (dual of [(2057, 7), 14155, 38]-NRT-code) | [i] | ||
| 8 | Linear OOA(2244, 2057, F2, 8, 37) (dual of [(2057, 8), 16212, 38]-NRT-code) | [i] | ||
| 9 | Digital (207, 244, 2057)-net over F2 | [i] | ||