Information on Result #1053894
Linear OOA(2237, 4108, F2, 4, 33) (dual of [(4108, 4), 16195, 34]-NRT-code), using OOA 4-folding based on linear OA(2237, 16432, F2, 33) (dual of [16432, 16195, 34]-code), using
- construction X applied to Ce(32) ⊂ Ce(26) [i] based on
- linear OA(2225, 16384, F2, 33) (dual of [16384, 16159, 34]-code), using an extension Ce(32) of the primitive narrow-sense BCH-code C(I) with length 16383 = 214−1, defining interval I = [1,32], and designed minimum distance d ≥ |I|+1 = 33 [i]
- linear OA(2183, 16384, F2, 27) (dual of [16384, 16201, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 16383 = 214−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [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
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(2237, 3573, F2, 5, 33) (dual of [(3573, 5), 17628, 34]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(2237, 3573, F2, 6, 33) (dual of [(3573, 6), 21201, 34]-NRT-code) | [i] | ||
| 3 | Linear OOA(2237, 3573, F2, 7, 33) (dual of [(3573, 7), 24774, 34]-NRT-code) | [i] | ||
| 4 | Linear OOA(2237, 3573, F2, 8, 33) (dual of [(3573, 8), 28347, 34]-NRT-code) | [i] | ||
| 5 | Digital (204, 237, 3573)-net over F2 | [i] | ||