Information on Result #1053673
Linear OOA(2223, 4108, F2, 4, 31) (dual of [(4108, 4), 16209, 32]-NRT-code), using OOA 4-folding based on linear OA(2223, 16432, F2, 31) (dual of [16432, 16209, 32]-code), using
- construction X applied to Ce(30) ⊂ Ce(24) [i] based on
- linear OA(2211, 16384, F2, 31) (dual of [16384, 16173, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 16383 = 214−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(2169, 16384, F2, 25) (dual of [16384, 16215, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 16383 = 214−1, 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
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(2223, 3584, F2, 5, 31) (dual of [(3584, 5), 17697, 32]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(2223, 3584, F2, 6, 31) (dual of [(3584, 6), 21281, 32]-NRT-code) | [i] | ||
| 3 | Linear OOA(2223, 3584, F2, 7, 31) (dual of [(3584, 7), 24865, 32]-NRT-code) | [i] | ||
| 4 | Linear OOA(2223, 3584, F2, 8, 31) (dual of [(3584, 8), 28449, 32]-NRT-code) | [i] | ||
| 5 | Digital (192, 223, 3584)-net over F2 | [i] | ||