Information on Result #1096677
Linear OOA(2208, 6563, F2, 5, 27) (dual of [(6563, 5), 32607, 28]-NRT-code), using OOA 5-folding based on linear OA(2208, 32815, F2, 27) (dual of [32815, 32607, 28]-code), using
- discarding factors / shortening the dual code based on linear OA(2208, 32816, F2, 27) (dual of [32816, 32608, 28]-code), using
- construction X applied to Ce(26) ⊂ Ce(20) [i] based on
- linear OA(2196, 32768, F2, 27) (dual of [32768, 32572, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 32767 = 215−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(2151, 32768, F2, 21) (dual of [32768, 32617, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 32767 = 215−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [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(26) ⊂ Ce(20) [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(2208, 6563, F2, 6, 27) (dual of [(6563, 6), 39170, 28]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(2208, 6563, F2, 7, 27) (dual of [(6563, 7), 45733, 28]-NRT-code) | [i] | ||
| 3 | Linear OOA(2208, 6563, F2, 8, 27) (dual of [(6563, 8), 52296, 28]-NRT-code) | [i] | ||
| 4 | Digital (181, 208, 6563)-net over F2 | [i] | ||