Information on Result #1054298
Linear OOA(2236, 2051, F2, 4, 37) (dual of [(2051, 4), 7968, 38]-NRT-code), using OOA 4-folding based on linear OA(2236, 8204, F2, 37) (dual of [8204, 7968, 38]-code), using
- discarding factors / shortening the dual code based on linear OA(2236, 8206, F2, 37) (dual of [8206, 7970, 38]-code), using
- construction X applied to Ce(36) ⊂ Ce(34) [i] based on
- linear OA(2235, 8192, F2, 37) (dual of [8192, 7957, 38]-code), using an extension Ce(36) of the primitive narrow-sense BCH-code C(I) with length 8191 = 213−1, defining interval I = [1,36], and designed minimum distance d ≥ |I|+1 = 37 [i]
- linear OA(2222, 8192, F2, 35) (dual of [8192, 7970, 36]-code), using an extension Ce(34) of the primitive narrow-sense BCH-code C(I) with length 8191 = 213−1, defining interval I = [1,34], and designed minimum distance d ≥ |I|+1 = 35 [i]
- linear OA(21, 14, F2, 1) (dual of [14, 13, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(21, s, F2, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X applied to Ce(36) ⊂ Ce(34) [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(2236, 2051, F2, 4, 36) (dual of [(2051, 4), 7968, 37]-NRT-code) | [i] | Strength Reduction for OOAs | |
| 2 | Linear OOA(2237, 2051, F2, 4, 37) (dual of [(2051, 4), 7967, 38]-NRT-code) | [i] | OOA Duplication | |
| 3 | Linear OOA(2236, 1900, F2, 5, 37) (dual of [(1900, 5), 9264, 38]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 4 | Linear OOA(2236, 1900, F2, 6, 37) (dual of [(1900, 6), 11164, 38]-NRT-code) | [i] | ||
| 5 | Linear OOA(2236, 1900, F2, 7, 37) (dual of [(1900, 7), 13064, 38]-NRT-code) | [i] | ||
| 6 | Linear OOA(2236, 1900, F2, 8, 37) (dual of [(1900, 8), 14964, 38]-NRT-code) | [i] | ||
| 7 | Digital (199, 236, 1900)-net over F2 | [i] | ||