Information on Result #808997
Linear OOA(2254, 1046, F2, 2, 44) (dual of [(1046, 2), 1838, 45]-NRT-code), using OOA 2-folding based on linear OA(2254, 2092, F2, 44) (dual of [2092, 1838, 45]-code), using
- 1 times truncation [i] based on linear OA(2255, 2093, F2, 45) (dual of [2093, 1838, 46]-code), using
- construction X applied to Ce(44) ⊂ Ce(38) [i] based on
- linear OA(2243, 2048, F2, 45) (dual of [2048, 1805, 46]-code), using an extension Ce(44) of the primitive narrow-sense BCH-code C(I) with length 2047 = 211−1, defining interval I = [1,44], and designed minimum distance d ≥ |I|+1 = 45 [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(212, 45, F2, 5) (dual of [45, 33, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(212, 48, F2, 5) (dual of [48, 36, 6]-code), using
- adding a parity check bit [i] based on linear OA(211, 47, F2, 4) (dual of [47, 36, 5]-code), using
- extracting embedded orthogonal array [i] based on digital (7, 11, 47)-net over F2, using
- adding a parity check bit [i] based on linear OA(211, 47, F2, 4) (dual of [47, 36, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(212, 48, F2, 5) (dual of [48, 36, 6]-code), using
- construction X applied to Ce(44) ⊂ 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(2258, 1048, F2, 2, 44) (dual of [(1048, 2), 1838, 45]-NRT-code) | [i] | NRT-Code Embedding in Larger Space | |
| 2 | Linear OOA(2260, 1049, F2, 2, 44) (dual of [(1049, 2), 1838, 45]-NRT-code) | [i] | ||
| 3 | Linear OOA(2254, 1046, F2, 3, 44) (dual of [(1046, 3), 2884, 45]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 4 | Linear OOA(2254, 1046, F2, 4, 44) (dual of [(1046, 4), 3930, 45]-NRT-code) | [i] | ||
| 5 | Linear OOA(2254, 1046, F2, 5, 44) (dual of [(1046, 5), 4976, 45]-NRT-code) | [i] | ||
| 6 | Linear OOA(2254, 1046, F2, 6, 44) (dual of [(1046, 6), 6022, 45]-NRT-code) | [i] | ||
| 7 | Linear OOA(2254, 1046, F2, 7, 44) (dual of [(1046, 7), 7068, 45]-NRT-code) | [i] | ||
| 8 | Linear OOA(2254, 1046, F2, 8, 44) (dual of [(1046, 8), 8114, 45]-NRT-code) | [i] | ||
| 9 | Digital (210, 254, 1046)-net over F2 | [i] | ||