Information on Result #2422608
Linear OOA(2178, 1046, F2, 2, 30) (dual of [(1046, 2), 1914, 31]-NRT-code), using strength reduction based on linear OOA(2178, 1046, F2, 2, 31) (dual of [(1046, 2), 1914, 32]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2178, 2092, F2, 31) (dual of [2092, 1914, 32]-code), using
- discarding factors / shortening the dual code based on linear OA(2178, 2093, F2, 31) (dual of [2093, 1915, 32]-code), using
- construction X applied to Ce(30) ⊂ Ce(24) [i] based on
- linear OA(2166, 2048, F2, 31) (dual of [2048, 1882, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 2047 = 211−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(2133, 2048, F2, 25) (dual of [2048, 1915, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 2047 = 211−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [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(30) ⊂ Ce(24) [i] based on
- discarding factors / shortening the dual code based on linear OA(2178, 2093, F2, 31) (dual of [2093, 1915, 32]-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 OOA(2178, 963, F2, 3, 30) (dual of [(963, 3), 2711, 31]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(2178, 963, F2, 4, 30) (dual of [(963, 4), 3674, 31]-NRT-code) | [i] | ||
| 3 | Linear OOA(2178, 963, F2, 5, 30) (dual of [(963, 5), 4637, 31]-NRT-code) | [i] | ||
| 4 | Linear OOA(2178, 963, F2, 6, 30) (dual of [(963, 6), 5600, 31]-NRT-code) | [i] | ||
| 5 | Linear OOA(2178, 963, F2, 7, 30) (dual of [(963, 7), 6563, 31]-NRT-code) | [i] | ||
| 6 | Linear OOA(2178, 963, F2, 8, 30) (dual of [(963, 8), 7526, 31]-NRT-code) | [i] | ||
| 7 | Digital (148, 178, 963)-net over F2 | [i] | ||