Information on Result #1593869
Linear OOA(2181, 2437, F2, 4, 26) (dual of [(2437, 4), 9567, 27]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(2181, 2437, F2, 3, 26) (dual of [(2437, 3), 7130, 27]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2181, 2746, F2, 3, 26) (dual of [(2746, 3), 8057, 27]-NRT-code), using
- OOA 3-folding [i] based on linear OA(2181, 8238, F2, 26) (dual of [8238, 8057, 27]-code), using
- discarding factors / shortening the dual code based on linear OA(2181, 8239, F2, 26) (dual of [8239, 8058, 27]-code), using
- 1 times truncation [i] based on linear OA(2182, 8240, F2, 27) (dual of [8240, 8058, 28]-code), using
- construction X applied to Ce(26) ⊂ Ce(20) [i] based on
- linear OA(2170, 8192, F2, 27) (dual of [8192, 8022, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 8191 = 213−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(2131, 8192, F2, 21) (dual of [8192, 8061, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 8191 = 213−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [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(26) ⊂ Ce(20) [i] based on
- 1 times truncation [i] based on linear OA(2182, 8240, F2, 27) (dual of [8240, 8058, 28]-code), using
- discarding factors / shortening the dual code based on linear OA(2181, 8239, F2, 26) (dual of [8239, 8058, 27]-code), using
- OOA 3-folding [i] based on linear OA(2181, 8238, F2, 26) (dual of [8238, 8057, 27]-code), using
Mode: 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(2181, 1218, F2, 7, 26) (dual of [(1218, 7), 8345, 27]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(2181, 1218, F2, 8, 26) (dual of [(1218, 8), 9563, 27]-NRT-code) | [i] | ||