Information on Result #2480632
Linear OOA(2241, 1039, F2, 2, 42) (dual of [(1039, 2), 1837, 43]-NRT-code), using 21 times duplication based on linear OOA(2240, 1039, F2, 2, 42) (dual of [(1039, 2), 1838, 43]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(2238, 1038, F2, 2, 42) (dual of [(1038, 2), 1838, 43]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2238, 2076, F2, 42) (dual of [2076, 1838, 43]-code), using
- strength reduction [i] based on linear OA(2238, 2076, F2, 43) (dual of [2076, 1838, 44]-code), using
- construction X applied to Ce(42) ⊂ Ce(38) [i] based on
- linear OA(2232, 2048, F2, 43) (dual of [2048, 1816, 44]-code), using an extension Ce(42) of the primitive narrow-sense BCH-code C(I) with length 2047 = 211−1, defining interval I = [1,42], and designed minimum distance d ≥ |I|+1 = 43 [i]
- linear OA(2210, 2048, F2, 39) (dual of [2048, 1838, 40]-code), using an extension Ce(38) of the primitive narrow-sense BCH-code C(I) with length 2047 = 211−1, defining interval I = [1,38], and designed minimum distance d ≥ |I|+1 = 39 [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(42) ⊂ Ce(38) [i] based on
- strength reduction [i] based on linear OA(2238, 2076, F2, 43) (dual of [2076, 1838, 44]-code), using
- OOA 2-folding [i] based on linear OA(2238, 2076, F2, 42) (dual of [2076, 1838, 43]-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(2241, 1021, F2, 3, 42) (dual of [(1021, 3), 2822, 43]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(2241, 1021, F2, 4, 42) (dual of [(1021, 4), 3843, 43]-NRT-code) | [i] | ||
| 3 | Linear OOA(2241, 1021, F2, 5, 42) (dual of [(1021, 5), 4864, 43]-NRT-code) | [i] | ||
| 4 | Linear OOA(2241, 1021, F2, 6, 42) (dual of [(1021, 6), 5885, 43]-NRT-code) | [i] | ||
| 5 | Linear OOA(2241, 1021, F2, 7, 42) (dual of [(1021, 7), 6906, 43]-NRT-code) | [i] | ||
| 6 | Linear OOA(2241, 1021, F2, 8, 42) (dual of [(1021, 8), 7927, 43]-NRT-code) | [i] | ||
| 7 | Digital (199, 241, 1021)-net over F2 | [i] | ||