Information on Result #2227042
Linear OA(2252, 4143, F2, 40) (dual of [4143, 3891, 41]-code), using 1 times truncation based on linear OA(2253, 4144, F2, 41) (dual of [4144, 3891, 42]-code), using
- construction X applied to Ce(40) ⊂ Ce(34) [i] based on
- linear OA(2241, 4096, F2, 41) (dual of [4096, 3855, 42]-code), using an extension Ce(40) of the primitive narrow-sense BCH-code C(I) with length 4095 = 212−1, defining interval I = [1,40], and designed minimum distance d ≥ |I|+1 = 41 [i]
- linear OA(2205, 4096, F2, 35) (dual of [4096, 3891, 36]-code), using an extension Ce(34) of the primitive narrow-sense BCH-code C(I) with length 4095 = 212−1, defining interval I = [1,34], and designed minimum distance d ≥ |I|+1 = 35 [i]
- 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
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 OA(2255, 4146, F2, 40) (dual of [4146, 3891, 41]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(2256, 4147, F2, 40) (dual of [4147, 3891, 41]-code) | [i] | ||
| 3 | Linear OA(2257, 4148, F2, 40) (dual of [4148, 3891, 41]-code) | [i] | ||
| 4 | Linear OA(2258, 4149, F2, 40) (dual of [4149, 3891, 41]-code) | [i] | ||
| 5 | Linear OOA(2252, 2071, F2, 2, 40) (dual of [(2071, 2), 3890, 41]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(2252, 1381, F2, 3, 40) (dual of [(1381, 3), 3891, 41]-NRT-code) | [i] | ||
| 7 | Linear OOA(2252, 1035, F2, 4, 40) (dual of [(1035, 4), 3888, 41]-NRT-code) | [i] | ||
| 8 | Linear OOA(2252, 828, F2, 5, 40) (dual of [(828, 5), 3888, 41]-NRT-code) | [i] | ||
| 9 | Linear OOA(2252, 690, F2, 6, 40) (dual of [(690, 6), 3888, 41]-NRT-code) | [i] | ||
| 10 | Linear OOA(2252, 591, F2, 7, 40) (dual of [(591, 7), 3885, 41]-NRT-code) | [i] | ||
| 11 | Linear OOA(2252, 517, F2, 8, 40) (dual of [(517, 8), 3884, 41]-NRT-code) | [i] | ||