Information on Result #2668414
Linear OOA(2219, 2743, F2, 3, 32) (dual of [(2743, 3), 8010, 33]-NRT-code), using 1 times NRT-code embedding in larger space based on linear OOA(2216, 2742, F2, 3, 32) (dual of [(2742, 3), 8010, 33]-NRT-code), using
- OOA 3-folding [i] based on linear OA(2216, 8226, F2, 32) (dual of [8226, 8010, 33]-code), using
- 2 times code embedding in larger space [i] based on linear OA(2214, 8224, F2, 32) (dual of [8224, 8010, 33]-code), using
- 1 times truncation [i] based on linear OA(2215, 8225, F2, 33) (dual of [8225, 8010, 34]-code), using
- construction X applied to C([0,16]) ⊂ C([0,14]) [i] based on
- 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(2183, 8193, F2, 29) (dual of [8193, 8010, 30]-code), using the expurgated narrow-sense BCH-code C(I) with length 8193 | 226−1, defining interval I = [0,14], and minimum distance d ≥ |{−14,−13,…,14}|+1 = 30 (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([0,16]) ⊂ C([0,14]) [i] based on
- 1 times truncation [i] based on linear OA(2215, 8225, F2, 33) (dual of [8225, 8010, 34]-code), using
- 2 times code embedding in larger space [i] based on linear OA(2214, 8224, F2, 32) (dual of [8224, 8010, 33]-code), 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 OOA(2219, 2332, F2, 4, 32) (dual of [(2332, 4), 9109, 33]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(2219, 2332, F2, 5, 32) (dual of [(2332, 5), 11441, 33]-NRT-code) | [i] | ||
| 3 | Linear OOA(2219, 2332, F2, 6, 32) (dual of [(2332, 6), 13773, 33]-NRT-code) | [i] | ||
| 4 | Linear OOA(2219, 2332, F2, 7, 32) (dual of [(2332, 7), 16105, 33]-NRT-code) | [i] | ||
| 5 | Linear OOA(2219, 2332, F2, 8, 32) (dual of [(2332, 8), 18437, 33]-NRT-code) | [i] | ||
| 6 | Digital (187, 219, 2332)-net over F2 | [i] | ||