Information on Result #1595870
Linear OOA(2207, 2390, F2, 4, 30) (dual of [(2390, 4), 9353, 31]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(2207, 2390, F2, 3, 30) (dual of [(2390, 3), 6963, 31]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2207, 2746, F2, 3, 30) (dual of [(2746, 3), 8031, 31]-NRT-code), using
- OOA 3-folding [i] based on linear OA(2207, 8238, F2, 30) (dual of [8238, 8031, 31]-code), using
- discarding factors / shortening the dual code based on linear OA(2207, 8239, F2, 30) (dual of [8239, 8032, 31]-code), using
- 1 times truncation [i] based on linear OA(2208, 8240, F2, 31) (dual of [8240, 8032, 32]-code), using
- construction X applied to Ce(30) ⊂ Ce(24) [i] based on
- linear OA(2196, 8192, F2, 31) (dual of [8192, 7996, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 8191 = 213−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(2157, 8192, F2, 25) (dual of [8192, 8035, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 8191 = 213−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [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(30) ⊂ Ce(24) [i] based on
- 1 times truncation [i] based on linear OA(2208, 8240, F2, 31) (dual of [8240, 8032, 32]-code), using
- discarding factors / shortening the dual code based on linear OA(2207, 8239, F2, 30) (dual of [8239, 8032, 31]-code), using
- OOA 3-folding [i] based on linear OA(2207, 8238, F2, 30) (dual of [8238, 8031, 31]-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(2207, 1195, F2, 7, 30) (dual of [(1195, 7), 8158, 31]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(2207, 1195, F2, 8, 30) (dual of [(1195, 8), 9353, 31]-NRT-code) | [i] | ||