Information on Result #2480238
Linear OOA(2215, 1048, F2, 2, 37) (dual of [(1048, 2), 1881, 38]-NRT-code), using 21 times duplication based on linear OOA(2214, 1048, F2, 2, 37) (dual of [(1048, 2), 1882, 38]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(2212, 1047, F2, 2, 37) (dual of [(1047, 2), 1882, 38]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2212, 2094, F2, 37) (dual of [2094, 1882, 38]-code), using
- construction X applied to Ce(36) ⊂ Ce(30) [i] based on
- linear OA(2199, 2048, F2, 37) (dual of [2048, 1849, 38]-code), using an extension Ce(36) of the primitive narrow-sense BCH-code C(I) with length 2047 = 211−1, defining interval I = [1,36], and designed minimum distance d ≥ |I|+1 = 37 [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(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(36) ⊂ Ce(30) [i] based on
- OOA 2-folding [i] based on linear OA(2212, 2094, F2, 37) (dual of [2094, 1882, 38]-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(2215, 992, F2, 3, 37) (dual of [(992, 3), 2761, 38]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(2215, 992, F2, 4, 37) (dual of [(992, 4), 3753, 38]-NRT-code) | [i] | ||
| 3 | Linear OOA(2215, 992, F2, 5, 37) (dual of [(992, 5), 4745, 38]-NRT-code) | [i] | ||
| 4 | Linear OOA(2215, 992, F2, 6, 37) (dual of [(992, 6), 5737, 38]-NRT-code) | [i] | ||
| 5 | Linear OOA(2215, 992, F2, 7, 37) (dual of [(992, 7), 6729, 38]-NRT-code) | [i] | ||
| 6 | Linear OOA(2215, 992, F2, 8, 37) (dual of [(992, 8), 7721, 38]-NRT-code) | [i] | ||
| 7 | Digital (178, 215, 992)-net over F2 | [i] | ||