Information on Result #808429
Linear OOA(2241, 2072, F2, 2, 38) (dual of [(2072, 2), 3903, 39]-NRT-code), using OOA 2-folding based on linear OA(2241, 4144, F2, 38) (dual of [4144, 3903, 39]-code), using
- strength reduction [i] based on linear OA(2241, 4144, F2, 39) (dual of [4144, 3903, 40]-code), using
- construction X applied to Ce(38) ⊂ Ce(32) [i] based on
- linear OA(2229, 4096, F2, 39) (dual of [4096, 3867, 40]-code), using an extension Ce(38) of the primitive narrow-sense BCH-code C(I) with length 4095 = 212−1, defining interval I = [1,38], and designed minimum distance d ≥ |I|+1 = 39 [i]
- linear OA(2193, 4096, F2, 33) (dual of [4096, 3903, 34]-code), using an extension Ce(32) of the primitive narrow-sense BCH-code C(I) with length 4095 = 212−1, defining interval I = [1,32], and designed minimum distance d ≥ |I|+1 = 33 [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
- construction X applied to Ce(38) ⊂ Ce(32) [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(2243, 2073, F2, 2, 38) (dual of [(2073, 2), 3903, 39]-NRT-code) | [i] | NRT-Code Embedding in Larger Space | |
| 2 | Linear OOA(2245, 2074, F2, 2, 38) (dual of [(2074, 2), 3903, 39]-NRT-code) | [i] | ||
| 3 | Linear OOA(2242, 2072, F2, 2, 38) (dual of [(2072, 2), 3902, 39]-NRT-code) | [i] | OOA Duplication | |
| 4 | Linear OOA(2241, 1530, F2, 3, 38) (dual of [(1530, 3), 4349, 39]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 5 | Linear OOA(2241, 1530, F2, 4, 38) (dual of [(1530, 4), 5879, 39]-NRT-code) | [i] | ||
| 6 | Linear OOA(2241, 1530, F2, 5, 38) (dual of [(1530, 5), 7409, 39]-NRT-code) | [i] | ||
| 7 | Linear OOA(2241, 1530, F2, 6, 38) (dual of [(1530, 6), 8939, 39]-NRT-code) | [i] | ||
| 8 | Linear OOA(2241, 1530, F2, 7, 38) (dual of [(1530, 7), 10469, 39]-NRT-code) | [i] | ||
| 9 | Linear OOA(2241, 1530, F2, 8, 38) (dual of [(1530, 8), 11999, 39]-NRT-code) | [i] | ||
| 10 | Digital (203, 241, 1530)-net over F2 | [i] | ||