Information on Result #1512590
Linear OOA(2156, 803, F2, 3, 27) (dual of [(803, 3), 2253, 28]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(2156, 803, F2, 2, 27) (dual of [(803, 2), 1450, 28]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2156, 1046, F2, 2, 27) (dual of [(1046, 2), 1936, 28]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2156, 2092, F2, 27) (dual of [2092, 1936, 28]-code), using
- discarding factors / shortening the dual code based on linear OA(2156, 2093, F2, 27) (dual of [2093, 1937, 28]-code), using
- construction X applied to Ce(26) ⊂ Ce(20) [i] based on
- linear OA(2144, 2048, F2, 27) (dual of [2048, 1904, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 2047 = 211−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(2111, 2048, F2, 21) (dual of [2048, 1937, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 2047 = 211−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [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(26) ⊂ Ce(20) [i] based on
- discarding factors / shortening the dual code based on linear OA(2156, 2093, F2, 27) (dual of [2093, 1937, 28]-code), using
- OOA 2-folding [i] based on linear OA(2156, 2092, F2, 27) (dual of [2092, 1936, 28]-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(2156, 401, F2, 6, 27) (dual of [(401, 6), 2250, 28]-NRT-code) | [i] | OOA Folding | |