Information on Result #1054108
Linear OOA(2251, 4108, F2, 4, 35) (dual of [(4108, 4), 16181, 36]-NRT-code), using OOA 4-folding based on linear OA(2251, 16432, F2, 35) (dual of [16432, 16181, 36]-code), using
- construction X applied to Ce(34) ⊂ Ce(28) [i] based on
- linear OA(2239, 16384, F2, 35) (dual of [16384, 16145, 36]-code), using an extension Ce(34) of the primitive narrow-sense BCH-code C(I) with length 16383 = 214−1, defining interval I = [1,34], and designed minimum distance d ≥ |I|+1 = 35 [i]
- linear OA(2197, 16384, F2, 29) (dual of [16384, 16187, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 16383 = 214−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [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(2251, 3581, F2, 5, 35) (dual of [(3581, 5), 17654, 36]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(2251, 3581, F2, 6, 35) (dual of [(3581, 6), 21235, 36]-NRT-code) | [i] | ||
| 3 | Linear OOA(2251, 3581, F2, 7, 35) (dual of [(3581, 7), 24816, 36]-NRT-code) | [i] | ||
| 4 | Linear OOA(2251, 3581, F2, 8, 35) (dual of [(3581, 8), 28397, 36]-NRT-code) | [i] | ||
| 5 | Digital (216, 251, 3581)-net over F2 | [i] | ||