Information on Result #947247
Linear OOA(2168, 687, F2, 3, 31) (dual of [(687, 3), 1893, 32]-NRT-code), using OOA 3-folding based on linear OA(2168, 2061, F2, 31) (dual of [2061, 1893, 32]-code), using
- 1 times code embedding in larger space [i] based on linear OA(2167, 2060, F2, 31) (dual of [2060, 1893, 32]-code), using
- construction X applied to Ce(30) ⊂ Ce(28) [i] based on
- linear OA(2166, 2048, F2, 31) (dual of [2048, 1882, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 2047 = 211−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(2155, 2048, F2, 29) (dual of [2048, 1893, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 2047 = 211−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [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(30) ⊂ Ce(28) [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(2171, 688, F2, 3, 31) (dual of [(688, 3), 1893, 32]-NRT-code) | [i] | NRT-Code Embedding in Larger Space | |
| 2 | Linear OOA(2169, 687, F2, 3, 31) (dual of [(687, 3), 1892, 32]-NRT-code) | [i] | OOA Duplication | |
| 3 | Linear OOA(2170, 687, F2, 3, 31) (dual of [(687, 3), 1891, 32]-NRT-code) | [i] | ||
| 4 | Linear OOA(2168, 687, F2, 4, 31) (dual of [(687, 4), 2580, 32]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 5 | Linear OOA(2168, 687, F2, 5, 31) (dual of [(687, 5), 3267, 32]-NRT-code) | [i] | ||
| 6 | Linear OOA(2168, 687, F2, 6, 31) (dual of [(687, 6), 3954, 32]-NRT-code) | [i] | ||
| 7 | Linear OOA(2168, 687, F2, 7, 31) (dual of [(687, 7), 4641, 32]-NRT-code) | [i] | ||
| 8 | Linear OOA(2168, 687, F2, 8, 31) (dual of [(687, 8), 5328, 32]-NRT-code) | [i] | ||
| 9 | Digital (137, 168, 687)-net over F2 | [i] | ||