Information on Result #807817
Linear OOA(2177, 1029, F2, 2, 32) (dual of [(1029, 2), 1881, 33]-NRT-code), using OOA 2-folding based on linear OA(2177, 2058, F2, 32) (dual of [2058, 1881, 33]-code), using
- discarding factors / shortening the dual code based on linear OA(2177, 2059, F2, 32) (dual of [2059, 1882, 33]-code), using
- 1 times truncation [i] based on linear OA(2178, 2060, F2, 33) (dual of [2060, 1882, 34]-code), using
- construction X applied to Ce(32) ⊂ Ce(30) [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(2166, 2048, F2, 31) (dual of [2048, 1882, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 2047 = 211−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(21, 12, F2, 1) (dual of [12, 11, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(21, s, F2, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X applied to Ce(32) ⊂ Ce(30) [i] based on
- 1 times truncation [i] based on linear OA(2178, 2060, F2, 33) (dual of [2060, 1882, 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(2177, 724, F2, 3, 32) (dual of [(724, 3), 1995, 33]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(2177, 724, F2, 4, 32) (dual of [(724, 4), 2719, 33]-NRT-code) | [i] | ||
| 3 | Linear OOA(2177, 724, F2, 5, 32) (dual of [(724, 5), 3443, 33]-NRT-code) | [i] | ||
| 4 | Linear OOA(2177, 724, F2, 6, 32) (dual of [(724, 6), 4167, 33]-NRT-code) | [i] | ||
| 5 | Linear OOA(2177, 724, F2, 7, 32) (dual of [(724, 7), 4891, 33]-NRT-code) | [i] | ||
| 6 | Linear OOA(2177, 724, F2, 8, 32) (dual of [(724, 8), 5615, 33]-NRT-code) | [i] | ||
| 7 | Digital (145, 177, 724)-net over F2 | [i] | ||