Information on Result #808798
Linear OOA(2233, 1030, F2, 2, 42) (dual of [(1030, 2), 1827, 43]-NRT-code), using OOA 2-folding based on linear OA(2233, 2060, F2, 42) (dual of [2060, 1827, 43]-code), using
- strength reduction [i] based on linear OA(2233, 2060, F2, 43) (dual of [2060, 1827, 44]-code), using
- construction X applied to Ce(42) ⊂ Ce(40) [i] based on
- 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(2221, 2048, F2, 41) (dual of [2048, 1827, 42]-code), using an extension Ce(40) of the primitive narrow-sense BCH-code C(I) with length 2047 = 211−1, defining interval I = [1,40], and designed minimum distance d ≥ |I|+1 = 41 [i]
- linear OA(21, 12, F2, 1) (dual of [12, 11, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(21, s, F2, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X applied to Ce(42) ⊂ Ce(40) [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(2235, 1031, F2, 2, 42) (dual of [(1031, 2), 1827, 43]-NRT-code) | [i] | NRT-Code Embedding in Larger Space | |
| 2 | Linear OOA(2234, 1030, F2, 2, 42) (dual of [(1030, 2), 1826, 43]-NRT-code) | [i] | OOA Duplication | |
| 3 | Linear OOA(2233, 879, F2, 3, 42) (dual of [(879, 3), 2404, 43]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 4 | Linear OOA(2233, 879, F2, 4, 42) (dual of [(879, 4), 3283, 43]-NRT-code) | [i] | ||
| 5 | Linear OOA(2233, 879, F2, 5, 42) (dual of [(879, 5), 4162, 43]-NRT-code) | [i] | ||
| 6 | Linear OOA(2233, 879, F2, 6, 42) (dual of [(879, 6), 5041, 43]-NRT-code) | [i] | ||
| 7 | Linear OOA(2233, 879, F2, 7, 42) (dual of [(879, 7), 5920, 43]-NRT-code) | [i] | ||
| 8 | Linear OOA(2233, 879, F2, 8, 42) (dual of [(879, 8), 6799, 43]-NRT-code) | [i] | ||
| 9 | Digital (191, 233, 879)-net over F2 | [i] | ||