Information on Result #808608
Linear OOA(2222, 1030, F2, 2, 40) (dual of [(1030, 2), 1838, 41]-NRT-code), using OOA 2-folding based on linear OA(2222, 2060, F2, 40) (dual of [2060, 1838, 41]-code), using
- strength reduction [i] based on linear OA(2222, 2060, F2, 41) (dual of [2060, 1838, 42]-code), using
- construction X applied to Ce(40) ⊂ Ce(38) [i] based on
- 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(2210, 2048, F2, 39) (dual of [2048, 1838, 40]-code), using an extension Ce(38) of the primitive narrow-sense BCH-code C(I) with length 2047 = 211−1, defining interval I = [1,38], and designed minimum distance d ≥ |I|+1 = 39 [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(40) ⊂ Ce(38) [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(2224, 1031, F2, 2, 40) (dual of [(1031, 2), 1838, 41]-NRT-code) | [i] | NRT-Code Embedding in Larger Space | |
| 2 | Linear OOA(2223, 1030, F2, 2, 40) (dual of [(1030, 2), 1837, 41]-NRT-code) | [i] | OOA Duplication | |
| 3 | Linear OOA(2222, 851, F2, 3, 40) (dual of [(851, 3), 2331, 41]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 4 | Linear OOA(2222, 851, F2, 4, 40) (dual of [(851, 4), 3182, 41]-NRT-code) | [i] | ||
| 5 | Linear OOA(2222, 851, F2, 5, 40) (dual of [(851, 5), 4033, 41]-NRT-code) | [i] | ||
| 6 | Linear OOA(2222, 851, F2, 6, 40) (dual of [(851, 6), 4884, 41]-NRT-code) | [i] | ||
| 7 | Linear OOA(2222, 851, F2, 7, 40) (dual of [(851, 7), 5735, 41]-NRT-code) | [i] | ||
| 8 | Linear OOA(2222, 851, F2, 8, 40) (dual of [(851, 8), 6586, 41]-NRT-code) | [i] | ||
| 9 | Digital (182, 222, 851)-net over F2 | [i] | ||