Information on Result #809190
Linear OOA(2260, 1038, F2, 2, 46) (dual of [(1038, 2), 1816, 47]-NRT-code), using OOA 2-folding based on linear OA(2260, 2076, F2, 46) (dual of [2076, 1816, 47]-code), using
- strength reduction [i] based on linear OA(2260, 2076, F2, 47) (dual of [2076, 1816, 48]-code), using
- construction X applied to Ce(46) ⊂ Ce(42) [i] based on
- linear OA(2254, 2048, F2, 47) (dual of [2048, 1794, 48]-code), using an extension Ce(46) of the primitive narrow-sense BCH-code C(I) with length 2047 = 211−1, defining interval I = [1,46], and designed minimum distance d ≥ |I|+1 = 47 [i]
- linear OA(2232, 2048, F2, 43) (dual of [2048, 1816, 44]-code), using an extension Ce(42) of the primitive narrow-sense BCH-code C(I) with length 2047 = 211−1, defining interval I = [1,42], and designed minimum distance d ≥ |I|+1 = 43 [i]
- linear OA(26, 28, F2, 3) (dual of [28, 22, 4]-code or 28-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 Ce(46) ⊂ Ce(42) [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(2260, 1019, F2, 3, 46) (dual of [(1019, 3), 2797, 47]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(2260, 1019, F2, 4, 46) (dual of [(1019, 4), 3816, 47]-NRT-code) | [i] | ||
| 3 | Linear OOA(2260, 1019, F2, 5, 46) (dual of [(1019, 5), 4835, 47]-NRT-code) | [i] | ||
| 4 | Linear OOA(2260, 1019, F2, 6, 46) (dual of [(1019, 6), 5854, 47]-NRT-code) | [i] | ||
| 5 | Linear OOA(2260, 1019, F2, 7, 46) (dual of [(1019, 7), 6873, 47]-NRT-code) | [i] | ||
| 6 | Linear OOA(2260, 1019, F2, 8, 46) (dual of [(1019, 8), 7892, 47]-NRT-code) | [i] | ||
| 7 | Digital (214, 260, 1019)-net over F2 | [i] | ||