Information on Result #1096955
Linear OOA(2237, 6563, F2, 5, 30) (dual of [(6563, 5), 32578, 31]-NRT-code), using OOA 5-folding based on linear OA(2237, 32815, F2, 30) (dual of [32815, 32578, 31]-code), using
- 1 times truncation [i] based on linear OA(2238, 32816, F2, 31) (dual of [32816, 32578, 32]-code), using
- construction X applied to Ce(30) ⊂ Ce(24) [i] based on
- linear OA(2226, 32768, F2, 31) (dual of [32768, 32542, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 32767 = 215−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(2181, 32768, F2, 25) (dual of [32768, 32587, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 32767 = 215−1, 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
- construction X applied to Ce(30) ⊂ Ce(24) [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(2237, 6563, F2, 6, 30) (dual of [(6563, 6), 39141, 31]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(2237, 6563, F2, 7, 30) (dual of [(6563, 7), 45704, 31]-NRT-code) | [i] | ||
| 3 | Linear OOA(2237, 6563, F2, 8, 30) (dual of [(6563, 8), 52267, 31]-NRT-code) | [i] | ||
| 4 | Digital (207, 237, 6563)-net over F2 | [i] | ||