Information on Result #2479820
Linear OOA(2191, 1047, F2, 2, 32) (dual of [(1047, 2), 1903, 33]-NRT-code), using 21 times duplication based on linear OOA(2190, 1047, F2, 2, 32) (dual of [(1047, 2), 1904, 33]-NRT-code), using
- strength reduction [i] based on linear OOA(2190, 1047, F2, 2, 33) (dual of [(1047, 2), 1904, 34]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2190, 2094, F2, 33) (dual of [2094, 1904, 34]-code), using
- construction X applied to Ce(32) ⊂ Ce(26) [i] based on
- linear OA(2177, 2048, F2, 33) (dual of [2048, 1871, 34]-code), using an extension Ce(32) of the primitive narrow-sense BCH-code C(I) with length 2047 = 211−1, defining interval I = [1,32], and designed minimum distance d ≥ |I|+1 = 33 [i]
- linear OA(2144, 2048, F2, 27) (dual of [2048, 1904, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 2047 = 211−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(213, 46, F2, 5) (dual of [46, 33, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(213, 63, F2, 5) (dual of [63, 50, 6]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 26−1, defining interval I = [0,3], and designed minimum distance d ≥ |I|+1 = 6 [i]
- discarding factors / shortening the dual code based on linear OA(213, 63, F2, 5) (dual of [63, 50, 6]-code), using
- construction X applied to Ce(32) ⊂ Ce(26) [i] based on
- OOA 2-folding [i] based on linear OA(2190, 2094, F2, 33) (dual of [2094, 1904, 34]-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(2191, 1027, F2, 3, 32) (dual of [(1027, 3), 2890, 33]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(2191, 1027, F2, 4, 32) (dual of [(1027, 4), 3917, 33]-NRT-code) | [i] | ||
| 3 | Linear OOA(2191, 1027, F2, 5, 32) (dual of [(1027, 5), 4944, 33]-NRT-code) | [i] | ||
| 4 | Linear OOA(2191, 1027, F2, 6, 32) (dual of [(1027, 6), 5971, 33]-NRT-code) | [i] | ||
| 5 | Linear OOA(2191, 1027, F2, 7, 32) (dual of [(1027, 7), 6998, 33]-NRT-code) | [i] | ||
| 6 | Linear OOA(2191, 1027, F2, 8, 32) (dual of [(1027, 8), 8025, 33]-NRT-code) | [i] | ||
| 7 | Digital (159, 191, 1027)-net over F2 | [i] | ||