Information on Result #1191756
Digital (41, 55, 1171)-net over F8, using net defined by OOA based on linear OOA(855, 1171, F8, 14, 14) (dual of [(1171, 14), 16339, 15]-NRT-code), using
- OA 7-folding and stacking [i] based on linear OA(855, 8197, F8, 14) (dual of [8197, 8142, 15]-code), using
- 1 times code embedding in larger space [i] based on linear OA(854, 8196, F8, 14) (dual of [8196, 8142, 15]-code), using
- trace code [i] based on linear OA(6427, 4098, F64, 14) (dual of [4098, 4071, 15]-code), using
- construction X applied to Ce(13) ⊂ Ce(12) [i] based on
- linear OA(6427, 4096, F64, 14) (dual of [4096, 4069, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(6425, 4096, F64, 13) (dual of [4096, 4071, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 4095 = 642−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(640, 2, F64, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(640, s, F64, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to Ce(13) ⊂ Ce(12) [i] based on
- trace code [i] based on linear OA(6427, 4098, F64, 14) (dual of [4098, 4071, 15]-code), using
- 1 times code embedding in larger space [i] based on linear OA(854, 8196, F8, 14) (dual of [8196, 8142, 15]-code), using
Mode: Constructive and linear.
Optimality
Show details for fixed k and m, k and s, k and t, m and s, m and t, t and s.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Digital (42, 56, 1171)-net over F8 | [i] | Net Duplication | |
| 2 | Digital (43, 57, 1171)-net over F8 | [i] | ||