Information on Result #2479750
Linear OOA(2176, 1040, F2, 2, 31) (dual of [(1040, 2), 1904, 32]-NRT-code), using 2 times NRT-code embedding in larger space based on linear OOA(2172, 1038, F2, 2, 31) (dual of [(1038, 2), 1904, 32]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2172, 2076, F2, 31) (dual of [2076, 1904, 32]-code), using
- construction X applied to Ce(30) ⊂ Ce(26) [i] based on
- 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(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(26, 28, F2, 3) (dual of [28, 22, 4]-code or 28-cap in PG(5,2)), using
- discarding factors / shortening the dual code based on linear OA(26, 32, F2, 3) (dual of [32, 26, 4]-code or 32-cap in PG(5,2)), using
- construction X applied to Ce(30) ⊂ Ce(26) [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(2176, 799, F2, 3, 31) (dual of [(799, 3), 2221, 32]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(2176, 799, F2, 4, 31) (dual of [(799, 4), 3020, 32]-NRT-code) | [i] | ||
| 3 | Linear OOA(2176, 799, F2, 5, 31) (dual of [(799, 5), 3819, 32]-NRT-code) | [i] | ||
| 4 | Linear OOA(2176, 799, F2, 6, 31) (dual of [(799, 6), 4618, 32]-NRT-code) | [i] | ||
| 5 | Linear OOA(2176, 799, F2, 7, 31) (dual of [(799, 7), 5417, 32]-NRT-code) | [i] | ||
| 6 | Linear OOA(2176, 799, F2, 8, 31) (dual of [(799, 8), 6216, 32]-NRT-code) | [i] | ||
| 7 | Digital (145, 176, 799)-net over F2 | [i] | ||